Yes, it can be a bit much to learn all at once. You might want to start with these Pool School articles:
Recommended Chemicals and
How to Chlorinate.
Now, those articles are written for larger permanent pools. Your pool is small enough that that the usual recommendations don't apply so well. In your case I would suggest getting a form of chlorine where the ingredient list says "sodium dichloro-somethingorother" which comes in many brand names; we call it dichlor. This is a combination of chlorine and stabilizer, and you need both. So, get 3 pounds of dichlor, and use that as your chlorine source until it's all gone. After that, switch to bleach.
Are you using test strips? You probably also want one of the 2-way kits, chlorine and pH, that will be enough. Because the pool is green, you want to use the dichlor to get your chlorine up over 5, and keep the filter on, until the green clears up.
This might not be adequate, but with a little bit of luck it'll clear up and you won't need one of the heftier test kits.
Let us know how it goes, I want to find out if I'm a clever dude or a chump!
--paulr
