Although we of think of, and measure air sealing as reducing air flow, the real concern isn't with the air itself (in fact we're generally happy to have air flow), but the heat that is carried away with escaping air, and in some sense even more importantly, the moisture that moves along with the air.
From the standpoint of energy use, all air sealing is equal in that a tighter house equates to less energy use, but in the case of moisture all air sealing is definitely not equal--the only air movement that will cause a problem is where air moves thru a cavity where it can spread out and result in condensation. For example, air leaking out a bath fan vent isn't likely cause mold, but air leaking thru fluffy insulation is because the air pools in the cavity, if there is a cool enough air, the moisture condenses out (see condensing potential).
Air leaks mostly occur at the joints between materials in the envelope: around windows and doors, around holes drilled for pipes, wires and ducts, and in joints between sheets of plywood, in the rim joists, etc. Dense insulation like spray foam, or to a lesser degree dense pack cellulose, reduce some joint infiltration, and weaather barriers like Tyvek or asphalt building paper reduce the pressure on joints due to wind, but are not really considered air barriers any more unless the joints are taped or otherwise sealed. To get air tightness, joints need to be sealed with weather stripping, caulk, spray foam or any equivalent product. The more that get sealed, the tighter the building will be.
Most of them can be found by a careful visual inspection after framing and before insulation is installed. Using a blower door to reduce house pressure, air tightening specialists use smoke sticks to find leaks.
From a practical standpoint, tightening is easy up to a point, and then gets progressively more difficult unless the construction technique is inherently tight (eg SIP, spray foam). It is fairly easy to achieve 3ACH50, and not terribly hard to get to 2ACH50, but beyond there will require some work (at least until there is a standard practice on how to do so). The passive house standard of .6ACH50 will both challenge builders, and result in standard practices that allow create a clear path to tight buildings (assuming the level of interest in passive houses stay high).
There are four classes of material that are used for air sealing: caulks, spray foam, tape and mastic. There are two key properties of an air sealing material, that is sticks well and that is has some flexibility so when components move a little the joint doesn't pop open. Everyone has their own preferences and biases about what sealing material to use, so this guideline is inherently vague.
Caulks: beware of cheap caulks that won't stay flexible. Caulk is good for sealing tight joints, particularly when the gap is less than 1/4", and typically much less. Caulk is especially good when one material needs to be sealed to the other, like sealing drywall to a stud, or window flashing to the sheathing. Most caulks come in relatively small tubes, which means you end up buying cases of the.
Spray foam: cures to a rigid blob with minimal flexibility, but is a very strong glue There are two varieties: expanding and non-expanding, where really they both expand, but the non-expanding expands much less. Spray foam used to be the sealant of choice, but many builders are now using tape in places that used to be foamed, especially those who don't like the environmental footprint of spray foam (which is substantial). Typically application is holes that are larger than 1/4", especially when there is a deep hole, like a wire hole thru a 2x4, that can be filled. In addition to be used around wire and pipe holes, spray foam has been used around ducts penetrations, and to seal plywood sheathing to the framing, and occasionally to seal plywood joints as well. Spray foam mostly comes in cans, and they tend to be of the "use once" variety because the nozzle gets plugged up after the first use. Non-expanding foam is used around windows and door jambs, where expansion would push something out of plumb. One of the problems with expanding spray foam is that you can't really tell want happened underneath: is there a blob of foam on the surface because the hole is filled, or did it not even go in the hole? It's not always easy to control, and nearly impossible to do upside down.
Tapes: these are newer on the market, and early adopter used generic tapes that were not necessarily made for air sealing, but now more people are used specialty tapes designed for air sealing, which unfortunately are largely imported and are fairly expensive. The biggest problem with tapes are with stickiness, especially to the rough side of OSB, which has a notoriously loose surface. The biggest advantage is in high flexibility. How well they stick depends not only on the tape and substrate, but what conditions its applied in, particularly temperature and dryness, but as with all tapes, a clean surface is assumed.
Liquid applied membranes: these are like thick paints that are sprayed, rolled, brushed or troweled on.
Mastic: this is mostly used to seal ducts but can be used in places where caulks are used, ie small joints. Mastic comes in can and is applied with a brush.
Backer rods: these are some kind of foam rod that usually come in rolls of various widths. They are used to fill larger gaps and are usually covered with caulk or liquid applied membrane (ie some thick gooey material).
There are essentially three general approaches to air sealing: the barrier is at the plane of the drywall, the barrier is somewhere inside the wall or the barrier is on the outside of the sheathing. In each of these cases you will be sealing the cracks between sheathing materials, joints at sill plates, jointed around windows and door, and all penetrations (wires, pipes, ducts) as well.
Some building techniques result in inherently more air tight buildings than others: SIPs and ICFs for example typically have very tight joints. Stucco exterior is continuous so it makes a decent air barrier. If you use these, you'll need to do less air sealing.
None of these methods deals with sealing an unconditioned crawl space or basement--some other method will be needed for that, although with an unconditioned basement you could use air-tight drywall on the ceiling. You will also want to install a gasket under the sill plate--many builders use rolls of thin foam.
Housewrap is sometimes thought of as an air barrier but its not really one because there are too many leaky joints. Housewrap tends to do a better job of stopping air from coming in than it does air going out, because inward air movement pulls the housewrap joints tight against the sheathing. Housewrap can help a very leaking building, but it will do little for a somewhat tight one.
Dense pack cellulose insulation is also thought of as providing an air barrier, but it also is not. Again, it will slow air movement somewhat, but it won't stop it. Spray foam insulation, on the other hand is an air barrier.
Air tight drywall: in this technique, air sealing is done at the drywall layer. Before installing drywall, caulk the bottom plate to the subfloor. Then as you're installing drywall, you need to run a bead of caulk along the bottom plate and around all windows and door edges, and squash the drywall into the wet caulk. In addition, every penetration of the drywall also has to be sealed, ie electrical boxes, can lights, duct holes and plumbing penetrations.
The biggest drawback to air-tight drywall is that its an extra step for the drywall crew that many are not used to, and there are often so many penetrations in the drywall, that sealing them all is tedious. In addition to sealing electrical boxes to the drywall (caulk again), the boxes themselves have to be sealed in the back: tape, caulk holes or smother the whole mess in spray foam. Ceiling can lights are especially difficult to seal. The floor above unheated crawlspaces or basements will need to be air sealed some other way, but luckily there is usually not typically much pressure difference between these two spaces (ie little air movement, and no stack effect pressure) unless the house uses exhaust-only or supply-only ventilation. This is also
Inside of wall: in this technique, the inside of the sheathing is the air barrier. The advantage of this method over air tight drywall is that there are less penetrations to seal around: usually just a small number of faucet pipes, exterior outlets and ducts for exhaust fans. The disadvantage is that except in cathedral ceilings, there is no easy way to make the air boundary continuous across the ceiling.
In most cases the only sealing that is done to is seal the sheathing the plate and around penetrations. The bottom plate also needs to be caulked to the subfloor. To get a full seal you would need to also seal around window and door openings, but since those are double studs, you won't get as good a seal.
If housewrap is used instead of sheathing, you can foam to the housewrap, but since the housewrap is flexible, its not clear how durable this connection will be.
If the sheathing layer is not on the exterior (as in with larsen trusses), you should still be able to air seal at this layer, it just means your air barrier is inside your wall.
The brute force version of this is to spray foam about 2" everywhere using professional equipment instead of a can. This generally gets it very tight, but you do have to think about the vapor issue as well.
Taped sheathing joints: this involves the same number of penetrations as sealing on the inside of the sheathing, so the real difference is using tape instead of spray foam. The big issue here is finding the right tape for whatever sheathing surface you have, or making sure the sheathing is installed with the side the tape sticks to facing out: OSB in particular has a smooth side and a rough side and tapes don't tend to stick to the rough side very well.
A new approach is to use specially treated sheathing that has a vapor permeable waterproof layer on it (an example is Zip Wall), and then there is a smooth surface to tape to and in this case the tape is both an air barrier and a water barrier. It does mean you're relying on the durability of the glue in the tape, since there are many vertical joints, and unlike with building paper or housewrap, there is no overlap at joints.
While some question the longevity of tapes, its not clear that foam or caulk lasts any longer, although the further the seal is from the exterior the less extreme temperatures it experiences. In terms of determining whether the air sealing has been done, tapes are the easiest to inspect.
Windows, doors and ventilation fans: unlike air leaks thru insulation, these leaks don't generally cause mold problems--they air flies out fast enough that the moisture in it doesn't have time to condense. There are two separate issues with windows and doors: the first is the quality of the gasket/weather strip that window or door comes with, and the second is the air sealing that in done around the window or door unit.
Ventilation fans are essentially just holes in the envelope, so in order to get a very tight building, the total number of openings in the envelope must be reduced. While the fan itself in a typical bath fan provides some resistance to air flow when its off, and HRV tends to provide more resistance when off (verify).
Air sealing is usually done after utility rough in but before insulation. Unless the insulation contractor does the air sealing, no one else will do it, so many contractors either do it themselves or use an specially trained employee to do it. Its best to run a blower door test after air sealing to see if you've missed anything, and also to see if you're hitting whatever target you have.