#1
I didn't start doing any alternate picking until just recently (I finally accepted that I needed to learn it if I was going to go any faster), and it's kinda awkward for me after a year of just picking to the floor to start doing both. What are some practice routines or general tips for alt picking?
#2
You want to get the fundamentals down first, when it's easiest. On a single string, then when you're confident with that - go to cross string mechanics. Really, there's too much to say in one post, so I'll just leave you with a few helpful clickies

Speed Mechanics - That has some extremely good alterate picking advice and excercises.

Guitar Principles. - Priceless advice to be had here, not just on alternate picking, but other techniques, too. How they're applied psychologically, and more importantly, the correct way to practice!

The Technique Thread - Some pretty useful advice in there on all things technique from the Shred Forum.

Anchor or No Anchor - That's there if you have any quams, misconceptions or doubts about your picking efficiency.

Relax and you can't go wrong.
#3
Three words:

1. Metronome
2.Metronome
3.Metronome
Practice slow at first then work your way up