1) Pet training as it was no longer exists. Pets now have a talent tree which operates exactly like player talent trees, though they only have one tab. The tab that a pet gets is determined by the pet type. There are three pet types with accompanying trees: ferocity, tenacity and cunning, which roughly match up to DPS, tanking and utility, respectively. You can access your pet's talent tree by opening your own talent tree and looking for a pet tab on the side or bottom, then spec away.
2) After you spec your pet, I imagine you will find that this improves, since its dps will improve and it will gain additional abilities to help it keep aggro. ADDITIONALLY, there is a major bug with pet abilities and autocasting at the moment. Pet abilities have their own spell tab, as before, and, after spec'ing, you will have MANY more pet abilities than you have space on your little pet bar.
For some reason, any pet ability that is NOT on your pet bar but IS in your spellbook will ALWAYS revert to having autocast on whenever you dismiss your pet-including death, mounting or taking a flightpath. So, since all pets have cower as a built in ability and since you probably don't have cower on your bar, it is possible that you pet is casting cower and reducing its aggro. It may or may not be autocasting all sorts of other silly things that you don't want it to. To make sure it stops doing that, you have to find space on your tiny, tiny pet bar to fit those abilities that you want to not have autocasting all the time.
Additionally, you can't just drag a pet ability to a normal action bar and have it function. Instead, you need to put the pet ability into a macro and then drag it to a normal action bar. This, of course, requires you to manually activate the ability, which might be rendered moot because the pet is trying to autocast it, unless you've found space for it on your pet bar or you bother to turn off autocast literally every time you summon your pet.
Groovy?
3) They are ridiculously powerful right now, especially for BM hunters. BM pets are currently doing 1500-2000 dps by themselves fully buffed in raid situations, which is why blizzard is nerfing them so hard. If you're BM, make liberal use of misdirect and intimidate to help it along if you're still having trouble with aggro after spec'ing your pet. They're both on much shorter cooldowns than they used to be.
And finally, check out this page
Petopia: Patch 3.0 - Overview for the major recent changes. It should give you a good overview about everything that's going on, as well as providing links to show you the different types of trees and the different pet families found within those trees and the type of family skill each family has. The system became MUCH more complex with 3.0, but there's a ton of variety for personalization, which is cool. Hopefully we can keep blizzard's grubby hands off our steadyshot, so that hunters can remain happy fun dps instead of tossing limp noodles around.