So my question is, with only 6 'tiers' of talents after MoP, what is happening to all the other talents that are currently in game? Are they going to be skills you learn from your class trainer, either active or passive? Or removed from the game completely?
A little of both. :)
To better explain, let's divide the current talents into five categories: 1) mandatory, 2) very cool, but not mandatory, 3) sort of cool, 4) boring, and 5) useless.
We're going to give you all of the "mandatory" talents to your class spec, and you'll learn those talents at certain levels like you do with core class spells. Players who skip over what we consider mandatory talents today -- like Raging Blow or Hot Streak -- are unintentionally (or maybe even intentionally) gimping themselves, and that's not what we want to have happen. We want players to be able to experience the full power of their class, so we're going to award certain talents straight-out.
The second category of talents -- the cool, but not mandatory ones -- are really the heart of the new talent system (they're the talents you'll probably be choosing from in each of new six tiers). You may be glad you have talent A, but talent B and talent C are also compelling options, and it should ideally be an interesting choice about which one you take and when.
The third category of talents are still pretty cool, but they just aren't at the same level as other talents. These talents make good glyphs. For example, an early version of the warrior tree had Rude Interruption as a talent, but we feel it's too situational to compete with the other talents, so we'll likely make it a glyph.
The next category are boring talents -- the kind that reduce cooldowns or increase damage on some abilities. In most cases, we're just baking talents these right into the spells themselves. While there were occasionally situations where you got to decide which of these talents to take, the answers often relied on complex math problems that some other player ended up solving for most of us.
Finally, the current trees (despite our best efforts) still have some bad talents. They're the talents you almost inevtiably end up with when you have a talent tree with X rows and Y columns that you need to populate. In the end, not a lot of players end up taking these talents, so we'll just cut them. We don't think they'll be missed, but if turns out that players wind up actually missing some of the Cataclysm talents in the Mist of Pandaria design, then we've probably made a mistake somewhere. Ideally, you won't miss a thing and will have more fun picking talents that cater to your play style (or, at the very least, the current situation.)