First building stairs isn’t the hardest thing, but you should really evaluate your skills. You are going to have to head off the joists, and if possible double up some floor joists under the stairs. There is some structural framing that needs to be done, so you may want to call a contractor on this one.
You need to get more info than I can supply here, try Hometime or this Old House websites, but I will give you the short answer for building stairs that are to be carpeted.
First you need to know floor-to-floor height. For this example, use standard height which is 8' 11-1/8" assuming standard wall height of 8' 1-1/8" (typ 8' ceiling) and 2x10 jsts and 3/4" decking.
Divide by 7-1/2" for each riser height, you get 14.283 risers. Since you can not have a partial riser you need to round to the closest riser, or 14 risers. Therefore, you need 14R @ 7.6518", or about 7-5/8". That leaves 3/8" difference.
You have one less tread than risers, because the upper floor acts like a tread. Therefore, 13 treads. The question is the width of the tread. Most builders use 10-1/4" tread, because they use a 2x12 for the tread. With 11-1/4" for a 2x12 and one inch nose, you get 10-1/4" level cut.
Remember that 3/8” difference. Add half (3/16”) that to the bottom riser. That way you split the difference between the top and bottom risers. Now on the bottom riser you subtract the thickness of the tread, in this case, 1-1/2”. That will make the first plumb
cut have a height of 5-15/16”. Using a framing square, step off the trends and risers. Set one tongue at the trend width of 10-1/4” and the other at 7-5/8” for the risers on a 2x12 stringer. The last tread width will be 9-1/2” because the header is the riser. Also you need to notch the bottom of the stringer at the riser for a 2x4, and the back side of the last plumb cut for a 2x4. Cut the stringer and use as template for two more stringers.
Assuming you have walls on both sides you need a 2x4 spacer that runs along the bottom of the stringer on the wall. What this does is allow the drywall and skirt board to slide down and still have 1/2” for the carpet to be tucked in. Stringers go up first, then first riser, using 1x8, then next riser. Then first tread. Use construction adhesive on the treads and along the back edge of the tread. Nail through the bottom of the riser in to the tread. This will prevent squeaks. Then go up the stairs, alternating treads and risers.
Now this example is for stairs that are to be carpeted and have walls on both sides. You will have to do things a little different if one side is open or wood stairs. But that should get you thinking do I really want to do it. If you need any other advice email me.
Email you address, only if you want, and I can send you a section detail of the method I'm talking about.