I don't get Frost Mage, I feel like I need to level one up to 60 to sort of understand how to play it.
A frost mage under lvl 60 does not have Frozen Orb, Brain Freeze(which makes your Frostfire Bolt instant once in a while) or the talents above lvl 60, so yeah, you're missing important stuff.
Not sure what you're not getting though. It's fairly simple... Spam Frostbolt, use Ice Lance and Frostfire bolt when you get procs, and cast Frozen Orb, Ice Nova and Comet Storm(if you chose the talents) on cooldown. But since you're missing more than half of this stuff under lvl 60... so, yeah. Too early for you to judge a spec.