There are a couple of things you can do. One is to bottle carbonate with a co2 tank, if you have it available. That's my preference, because with a carbonator cap it's super easy to do. But if you don't have a c02 tank, then it has to be done an "old fashioned" way.
To make the diet soda (or any soda), all you have to do is add some yeast. I like champagne yeast for this- it's clean and neutral flavored. You can get it from any LHBS and it's like $.49 cents a package. you only need about 1/2 teaspoon. You will need some sugar so the yeast can eat that, but then you can use splenda/stevia/saccharine/ for the majority of the sweetening.
I make a really good ginger ale (recipe posted under my avatar, and in the recipe database under "soda") and you could do that with splenda instead of most of the sugar. I bet that would come out great.