I need some advice as to how to keep my above ground pool clean.

[PoolDoc]

I have small black particles that build up at the bottom of my above ground pool on a daily basis. They are small, black and slimy and easily break up and dissolve if you step on them.

I need to know what causes them to form; only then will I be able to permanently deal with them.

It's very likely that the dots are caterpillar poop. If you have any sort of vegetation overhanging over the pool, it's almost certain. If you do not have any vegetation higher than the pool, within 10 feet of it, then we'll have to look for another explanation.

Also, I have a thin green slime that builds up on the side of my pool. After a week the slime becomes very noticeable. What causes the thin green slime to form?

Green slime is caused by algae . . . which results from inadequate chlorination. You need to read the "Best Guess" page, linked in my blue signature block, to understand what "correct" chlorine levels may not actually be correct. You'll almost certainly need a Taylor K2006 test kit in order to resolve the issue. These are not available locally, since it's hard to get pool dealers to sell something that tends to partially replace them, and definitely reduces their chemical sales.