The first thing your going to need is patience. Installing laminate or hardwood on stairs can be tedious and time consuming. This is a little different than installing solid stair treads. In a lot of cases folks want their stairs to match the surrounding laminate or hardwood flooring. If you decide to take on the task, the main objectives is are to cut the treads and stair noses as close as possible to the sides and make sure the stair nose, treads and risers are attached securely. (I use glue, construction adhesive and nails).
A lot of times the stairs have carpet on them, so removing the carpet can reveal some surprises. Such as the over hang on each stair (which may need to be removed) or the zillion staples the carpet guys used when install the carpet. Or maybe the treads under the carpet are warped or loose.
When preparing the stairs I remove all the staples, scrap any debris of such as drywall mud paint over spray etc. I also check for any treads that may not be flat. Sometimes this can be corrected with screws which are better than nails, nails tend to work loose. Or using a belt sander to get rid of high spots. Worse case would be to replace the tread with the same thickness board. And removing the over hang on each stair or fill in the space below the over hang.
Deciding on what type of riser is something that needs to be considered. You can either use the same flooring your installing on the treads or use a painted wood as a riser. 1 X pine or polar are good for this. Some folks like the stairs all the same, whereas others prefer the stairs to stand out more with the painted riser.
Consider the cost of the materials. Stair nosing can be costly, but you can usually get two stairs done with one length of nosing. Shop around for the best price of pine or poplar for the risers if you want that look. As far as the amount of flooring you will need, a typical stair is about 3 feet wide by about 1 foot deep. This is 3 square feet for the tread or 6 square feet if your doing the riser with the flooring also. Always add 10 percent extra when ordering your flooring. This extra flooring is needed for waste and when mistakes are made. Its good to have extra left over also in case of repairs that may need to be done in the future.
Using good quality tools can make the job easier. I use a sliding miter saw, nail gun, circular saw and table saw as well as various hand tools.
I will not use quarter round on the stairs to cover gaps. It does not look good and it makes your stairs smaller. If you have to cover gaps get some matching putty to fill them in. You will need some anyway to fill nail holes.
Anyway you look at it, its a lot of work. The more educated you are when you start, the better the finished job will look. It can be very rewarding when done the right way.