Janet's pretty much said it all except:

Do not be afraid to add bleach to your pool. It won't fade your liner unless you pour it down the side. The ways I like to add it are 3:
1) Slowly into the skimmer while the pump is on. Should take a minute to add a gallon jug.
2) Slowly into the return stream so it immediately pushes it around the pool.
3) Walking around the pool dribbling the bleach in at arm's length. Make the gallon last the whole perimeter.

All of these work and won't fade your liner.