Latex paint should be cleaned out of a brush with warm soapy water (dish soap works well). You need to use a fine tooth brush comb - a small wire brush - or a nail brush (I like a nail brush best).
Work soap and water into the bristles with your fingers - make sure you get it up into the ferrule (the metal band that holds the bristles) Having paint stuck in the ferrule is what ruins a brush.
Use your brush to work into the bristles and brush out - just as you would brush hair.
Your brush is clean when it looks like it hasn't been used. Pat it dry and put it back in its package (good brushes come with good packages) - this will help it keep its shape.
Hang it from a nail - or lay it flat - don't ever stand it on its bristles - even for a few minutes.
The paint you wash out won't hurt you pipes - but don't pour used paint down the drain - that will.
Also, don't ever pour paint thinner down the drain - it is like pouring oil down there - very bad for mother earth.
Any dirty solvent you use can be set aside - either to evaporate - or to let the paint settle out - you can use the solvent again by carefully pouring it off.
Rags need to be spread out - or hung to dry - leave them in a bunch and they are likely to start a fire!