The water pollution should be easily solved: place your sewage things downstream from the fresh water things, that way they won't take in polluted water.
This is the only cause of water pollution that I have come across so far.
As to the other pollution there are two types left: noise and ground. One major cause of ground/noise pollution is industry which has an equally straightforward solution: separate it from your residential areas so the suburban society doesn't complain.
Some other things like airports, trainstations and dump yards also cause these so you should consider putting them on the outskirts of cities and preferably with a buffer zone between residential areas.
On Skylineswiki there is a note that says
Pollution can be decreased by planting trees in polluted areas. And sound pollution produced by roads can be lowered by upgrading them; sound barriers for motorways, and trees for normal roads. Placing offices will reduce the amount of sound pollution. Buildings producing noise or ground pollution should be moved away from residential areas.
The way it's phrased it would indicate that trees (from the decoration tab) help with pollution. There is no source however so I would not rely on this until confirmed reliably.
I did notice myself that offices don't have as much issue with pollution as residential buildings but whether that is cause or effect is unclear. I personally like to use offices as a buffer zone between residential areas and industrial ones.
As to how you can remove it: simply don't build anything polluting and eventually the pollution will be gone. This is also the case for water pollution -- after upgrading to clean sewage, you'll notice that the stream of pollution moves away from your river and isn't replenished.