Check the books and videos. Library is free. You must understand how many steps it will have to know how far it's going to stick out. That goes to where the bottom landing will be, and so on and so forth. If you are just handy, this is not a project you can build safely. Handrail and balusters and their connections are especially important. Not splitting the connection points are also very important. Read up word by word on at least 3 instructional books because one book may not tell you everything you need to know.
You don't have to cut the stringers. Cleats can be bolted to the stringers for the treads to sit on. You can have 30" wide stairs with 2x treads with 2x12 stringers on each side. Any wider, Middle stringer should be cut. Rule is each step must be no higher than 7 1/2" high, and treads no narrower than 9 1/2".
You have to know what kinds of fasteners and how corrosion resistant they are in the treated wood.
By the way, if you give this job to a carpenter, do not allow coated nails in a nail gun for the final fastening. They have the least corrosion resistance. Main posts and stringers must have coated bolts rated for the treated wood or stainless.