Hi Brooke,
hopefully I can help get you started.
I did a quick calculation of your 15 ft round x 3 ft deep pool and it holds 4000 gallons of water.
How much of something to put in depends on how much water you have, and what chemical are in the water. Since its new, then there isnt much in there. So..
1st go ahead right now and add 18 ozs of concentrated bleach. No facny splashless or scented stuff. Just plain ol bleach. Let your pump run at least 20 minutes after adding the bleach so it can be mixed well.
Next, you need to go to walmart, home improvement, pool store, or anyplace pool products are sold. Buy come Stabilizer and Conditioner (we call it CYA). It is sold in 4 lb jugs. Buy one jug then come home. Pour 16 ozs of it into an old sock and tie the top of the sock closed so it cant come out. Then tie a string on the end of a pole and hang the sock in front of the return. Squeeze the sock occasionally to help the stabilizer excape the sock.
The day after you added 12 ozs of stabilizer add 12 ozs of bleach only.
Add 12 ozs every day until your test kit arrives. When your test kit arrives, test your water for all of the things to test for and tell us what the test results are. Then we can go from there.
In the mean time, play around with pool math. Its what we use to calculate how much of something to add to the water.
http://www.troublefreepool.com/calc.html
Also while you are waiting, start with the ABCs of pool chemistry in Pool School. Then continue reading pool school articles about how to maintain your water levels, and what they should be.