Typically the ones you see selling on the television channels are enhanced by irradiation (unless they say they're natural). Irradiated diamonds come in red, pink, blue, yellow, green and black. All black diamonds are irradiated. Browns/champagnes and other fancy names for brown diamonds are usually natural but not worth much.
Obviously natural diamonds are worth much more than enhanced diamonds and the colour is due to the chemical makeup. It is reasonably easy however to find natural yellow diamonds and of course, the more yellow the more £ you pay! Natural pinks in small sizes can be found also but when you start getting to .5ct upwards they become more difficult to source. Not impossible but more difficult.
Reds, blues and natural greens are very rarely seen apart from being sold by specialist dealers and then cost ££££££££££££££££££.
Please beware however, coated diamonds are unfortunately being seen more now. As far as I'm aware they're not being sold at Gems, TJC etc. However, Ebay is swamped with them. With coated diamonds, only the pavillion is coated and this can be scratched off fairly easily. You would think that as it's only the pavillion that's coated you'd be able to spot them fairly easily but unfortunately that's not the case. I think I posted up pictures of a natural, irradiated and coated pink diamond once before so if you do a search you might be able to find it. Also on Ebay you'll find diamonds that have been filled and clarity enhanced by lasers. Again, stay away as their stability is questionable.
Hope that helps.