Well, depending on the particulars of the design, stairs aren't really tremendously complex if you keep a few basic principles in mind. Think of the stair carriages as a single unit, with the treads merely "placed" (okay, they're fastened securely, but I tend not to rely on them for lateral stability) on the carriages.
The quickest and easiest place to find some pointers on stair building is in your local hardware store. Buy a 12" Swanson speed square; they are very handy for the project, and come with a little instruction book to help you out. Most of it focuses on roof construction, but it does include a section on stairs.
After that...a lot of the questions are best answered (IMO...especially for a Newbie) after hearing a bit more about the specifics of this staircase...height, width, tread depth, mobility, stuff like that.
Others are chiming in with construction specifics, so let me make one point that I've seen missed in many community theater sets: However you construct your stairs, make sure the risers are all the same height, at least within each unit.
Nothing is more disconcerting - or dangerous - for actors than to be going up and down stairs where the rise changes from 7" to 6" to 9" without warning. This is even more important for offstage escape stairs than it is for the ones visible to the audience. I've damned near killed myself on more than one occasion because somebody cobbled a set of escape steps together without paying attention to this little detail.
If you plan to keep the stairs in stock and think you might be building more in the future, making them all to standard rise (and to a lesser degree, tread) dimensions will make it *much* easier to use them as modules for future sets, too.
Regularity is all-important, both in the rise and in the tread. My stairs at home in London have a rise of 7" and a tread of 9 1/2". This is comfortable. Treads that are too narrow make descending difficult, as you may not have a big enough target for your foot. I have met stairs with 6" treads, and they are difficult to go down. You are liable to catch your heel on the step above. It is a help, if the decor allows, to put a white line at the edge of each step, particularly if the lighting is dim.
Secure handrails are a must. They should withstand a full body weight suddenly applied in any direction. You can't do this with huge, wide, processional steps, but these usually have low risers (6"), and generous steps (12"). Access stairs are a different question. These are always needed in multi-level sets. Their appearance is often of no consequence: their security and safety are. We have a number of treads which can be fitted to scaffold tube, with an angle adjustment. These are very good for high level access, from backstage.
Similar rise and run within a stair section is a necessity for ease and comfort... makes for less tripping than usual. When I have had to use two different sections of staircase with different rises and runs, I put a "transitional " platform or "landing" between them. Also tell the actors and whomever about the difference.
The building codes require minimum treads of 11" and maximum risers of 7" for most stairs. One and two family dwellings can be steeper under some codes, as can aisles in seating areas if required by sightlines.
Keep in mind the 7" X 11" are minimum and lesser risers and greater treads are safer. For the general populace, greater treads probably help more in preventing stumbles and resultant injuries from the stumbles than does lowering the rise. Lets face it, even on 11" treads, most of use have to turn our foot or let it overhang, both of which lessen stability. I've grown quite fond of a 6 1/2" by 13" or 13 1/2" stair as being very comfortable. Most of the so called formulas while cute and seemingly with the wisdom of tested lore, don't hold up under
Keep in mind that the measurement of the tread does not include the tread under the nosing but is the actual run dimension.
The building codes require the non-uniformity between the greatest and least not exceed 3/8", again the worst it can be for minimal safety, not a goal. This is usually a problem at tops and bottoms where the floor covering will change the rise. Since most falls happen in the first or last 3 steps, it is important to maintain uniformity in the first and last step.
Solid risers are desirable.
Non-uniformity and too short of tread ranks right up there with visibility for stair safety. Illumination, high contrast at nosings, glow tape, etc. all can help a lot if used well.
Besides the uniform 50 pounds linear foot in any direction at the top rail and 200 concentrated at one point on the top rail in any direction, the intermediate railings or panels or whatever fills in the space below the rail should be designed for 50 pounds per square foot. Equally important is the graspability of the rail. If you wouldn't want the handle on your hammer to be a 2 X 4 because it's hard to hold, don't use it for railings. You need to be able to get a good grip on it and remember that a hook hold, where you grab under and pull, is
equally important to stair safety as pressure downward. 1 1/4 pipe, 1 x 1 steel tube, 1 1/2 pipe at the largest, are all acceptable for hand rails. (Guards don't require graspability.)
Falls result in greater loss from injuries than vehicular accidents and possibly 100 times as great as from fire, and roughly half occur on stairs. It doesn't justify using a nail instead for a bolt because it takes another 5 minutes or not recutting the stringer.
A "nose" on a stair adds to the tripping hazard, as does a stair without a solid rise. If there's any kind of lip there, a toe can catch on it. Make the edges even, square and perpendicular at the edges. Use a small amount of glo-tape on the corners or edge to make them more visible. If you can, very SLIGHTLY round off the edges, shins will appreciate that and they seem to splinter less. A little sandbox sand added to the paint on the treads can give extra traction. One idea for the escape stairs is to run a string of rope lights along the offstage side
gives a low level of light and outlines each step. Do not use gloss paint (slippery, bad for lighting) nor carpeting/vinyl runners (tripping hazard).
I'd also suggest - when it's not possible/necessary to have a railing, always have a person there hand-guiding each person who goes up or down stairs. (My preference is a handsome gentleman in a tux!) I've seen folks trip on a two step unit going onto a 18" platform in a hotel ballroom. Not pretty.
Bob Syvanen, in Fine Homebuilding's _Stairs_, (Taunton Press, 1995) lists
these three formulas:
riser + tread = 17-1/2"
riser x tread = 75"
two risers + one tread = 24"
"All of them establish an incline between 33 and 37 degrees. This creates a stairway that is comfortable for most people."
Gregory Harrison, in the same book, says "These formulas have been eliminated from modern codes because they are far from perfect and exclude some safe designs. You should not rely on them." Earlier in his article, Harrison writes, "The minimum riser height by code is 4 in. and the maximum is about 8 in. Although I know of no code maximum for treads, unusually deep treads cause an abnormal gait that can cause missteps and a fall. The CABO One and Two Family Dwelling Code allows treads to be only 9 in. deep, which is ridiculous because almost all adult feet with shoes exceed this measurement,"
I've seen people fall walking on level floors. People fall walking up or down stairs that are built to any of the specs above. I'd say that consistent rise and run are an important key, as most people's feet clear the front of the tread by less than 3/8", and our feet and legs develop an expectancy for what comes next based on what has come before, even after just one or two steps.