Okay, 1st wave came from the 60's upto the late 70's. It was a clean mixture of Reggae and Jazz. The jazz side is where all those trumpets came from. Emphasis was placed on the instruments and not on the singing. The beat was slow and steady- ever heard of rock-steady? Well ska is what it came from. Some 1st wave bands were Laurel Aitken, Desmond Dekker, and King Edwards. If you wanna hear some 1st wave, search for one of these guys on the ska jukebox link.
2-Tone came from the late 70's to the late 80's. It wasn't too much faster than the 1st wave stuff, but it definitely changed. Ska became more popular as well as politically shocking. This was because of the rise of punks and skins who had a heavy influence on the ska community. Some 2-Tone bands are the Specials, the Selector, Madness, and the English Beat.
3rd wave is the stuff that is playing right now. It's punk influenced and usually the beat is a lot faster. Some bands are Oi influenced, if you don't know what Oi is- that's just too bad 'cuz I won't tell you. Anyways, some 3rd wave bands are the Toasters, Mustard Plug, the Suspects(one of our local bands), and the Skoidats.