Stairs
Stairs take up more space than most people realize, both in the space for the stairs themselves and the space for landings on both floors. You need to remember that a staircase exists on both floors, so whatever space it takes up on one floor the total space used is double. Because the space is already used, when there are multiple floors, the stairs should be staked on top of each other. In terms of efficiency a straight stair uses takes up the least space of any code-compliant stairway, but also creates the longest barrier.
Most building codes1 won't let you build stairs that are either too steep or too shallow. The average stair is somewhere around 7-1/2" high and 11" wide (usually called rise and run). Steps less than 7-1/4" feel a bit shallow, over 7-3/4" feel a bit steep. Most building codes2 won't let you go over 8". Likewise, a width less than 10-1/2" might seem a bit narrow, and more than 11-1/2 a bit wide. Codes generally won't allow anything less than 10" wide. Note that a 10" run will result in an 11" tread, since the tread sticks out 1". A common rule of thumb is that rise+run=17-18"; the idea being that shorter steps result in a longer leg swing than taller ones, but code does not necessarily require this.
Some people prefer the shorter 7" steps, but the general problem is that such a stairway occupies a larger footprint, and hence a larger building. Its probably safe to say it is not likely there will ever be general agreement on the topic. The whole issue of limiting stair design so that it accommodates the least common denominator of level of fitness and agility is quite offensive to some, and it fact it is not hard to find an older house with a greater than 8" rise.
The number of steps will always be one less than the number or risers, since the upper floor serves as the last step. To calculate the total rise, you need to add in the thickness of the floor, which will be between 8" and 12". For an eight foot ceiling you usually end up with 14-15 risers , and 15-16 for a nine foot ceiling. It is often the case that not every step is exactly the same (ie the space doesn't divide evenly), and in that case, a couple of steps are usually 1/8" higher or lower than the rest: in fact most building codes limit the difference between two adjacent steps to 1/8", and the difference between the tallest and shortest to 1/4". You generally have to provide at least 6'8" head clearance at every step.
Given these parameters, a straight stair of 14-15 steps occupies about 35SF for the stairs along and another 9SF minimum on each of the floors for landings: these landings could be part of a room or hall, but where ever they are, they still have to be kept clear, so the space can't be used for anything else, so essentially a stair will take up at least 44SF on each floor, or 88SF total. Other stair shapes, like the "L" or split staircase take up even more space because now one stair is replaced by a landing, which adds about 6.5SF to each floor. The "U" shape stair has a 3x6 landing (which is often more like 3x6.5), also replacing only one step, so it is yet another 9SF bigger than the "L". If the space on the upper floor is small enough (less than 250SF typ.) and not a bedroom, most jurisdictions will allow winder stairs in place of the midway landing, reducing the space penalty to 8SF per floor. Although these non-linear arrangements take more space, they create many more ways to place stairs in the overall layout, and may end up saving space overall if fitting the linear stairs forces other rooms to grow.
Also keep in mind that stairs often force there to be adjacent hallways. A typical scenario would be in a row house with the stairwell on the north wall--you exit the stairs either east or west but then need a hallway along the stairs to get to the other side of the building, so the 44SF the stairs takes becomes 88SF when you include a parallel hallway. In this case you might consider the 60SF U configuration.
If you call out the upper space on the plans as a loft, you can use very steep stairs--as steep as a ladder, which depending on width and angle occupies only 4-6SF of floor space. In this case building code is apparently OK that only agile bodied people can use it. A spiral staircase seem like a good solution, but the footprint of these for 36" wide treads is still about 28SF, or for 30" wide treads is about 20SF, so the savings is not that great. Plus good luck getting furniture up and down one. Needless to say, if you don't have to build code compliant stairs, you can put them in a smaller space: just don't forgot to make sure you can get furniture and the elderly you up and down them.
Because stairs occupy quite a bit of space, they cannot be placed just anywhere. For a linear set of stairs, they generally form an edge either along a wall or the stairs themselves are the wall. An "L" shaped stair will also run along a wall, but in the corner rather than on an edge. If there is not a long enough space, the "U" shaped stair can be placed as if it were a small room itself, or as part of a larger room.
Staircases often act as the transition between levels of intimacy, for example acting as the bridge between the common areas and bedrooms. Enclosing them completely tends to make them dark and a bit claustrophobic. Its best if they have some daylight into them, which can be achieved with a stairway window or just by opening up the walls on the top and bottom, which also has the effect of opening them up more like a funnel. Keep in mind that the more open they are, the more noise will carry between the floors, but also the easier warm air will flow out for stack effect cooling, so there is a tradeoff there.
Stairs can be a space on their own, functioning as a place to sit, if the bottom is wide enough, but you can get carried away with this. Those grand staircases may look impressive, but they're all space that mostly won't be used.
Stairs in Context
While its desirable to reduce the space used by stairs, its more important to consider how the stairs impact the overall layout--there is no point saving space if it messes up the layout of the rooms. The key consideration here is that rooms are typically between 10 and 15 feet, with 11-13 being the most common. If stair placement leaves a space that is only 8' or maybe 17' then you have to think about how you might use that less common space--some rooms like bath and laundry can fit in 8', but a bedroom won't fit in that very comfortably. Also consider that stairs are a major boundary that can't be crossed, so you typically want to place stairs either on an outside wall or at some central location where there would be a wall anyhow.
So the process is:
- Pick a stair type
- Find a location for it
- Add any hallways necessary for circulation
- Fill in rooms in the remaining space, repeat this process if they don't fit right
Notes
1: the stair code is annoyingly complex and like any other codes, subject to local variations, so take this discussion only as a generic guideline.
2: Commercial buildings are limited to 7" rise, while residential rise is limited to either 8", 7-3/4" or 7" depending on what base code is referred to. Apparently a lot of bad accidents happen on stairs, and the stair code has changed much to reflect this. On the other hand, one study I found implied that there were actually more accidents when there was only 1 or 2 steps (which don't require a rail and may not be controlled by the stair code)--largely because people weren't paying attention. This implies to me that small level changes between rooms is generally not a good idea. As for taller stairs, I'm fairly skeptical that the code changes will have much impact on accident rate: someday there will be actual data.