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?
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.
Three words:

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