[edit] Steps

Think about what you want to look like, and what reactions you want from others. You're aiming for different, but not so different that it makes people doubt your faith, if you make it known.
Go for the sort of odd but normal clothing (leather, denim, tartan pattern, camo). It’ll slide if you can find these in modest, yet still stylish brands. Band t-shirts. Hoodies.
Wear shoes, but they really don’t matter, as long as they basically match what you're wearing and aren’t too immature. Usually go for army surplus boots, like Doc Martens.
Mess with the hair; that really depends on what your parents allow so that you can have peace at home. Mohawks, now, are cool, and most parents don't mind that. Otherwise, just let your mom tousle your hair, and leave it that way if you like. Experiment with beading, braiding, ribbons, feathers. Dyeing: go for it.
Makeup -- for you women who can’t go without it: stay with your normal mascara, eyeliner, eyeshadow, unless you really have to change it.
Earring fads will pass. Don’t overdo it. Again, piercings depend on your parent’s limits, not yours.
Tattoo's are fine when you're of age. Remember: you are stuck with the same tat, but you can get a different t-shirt... You can get things that really reflect your faith. It's a personal decision and relies on your own convictions. Your body is the Temple of God, show your faith through that.
The music you listen to should reflect your faith. Try looking at www.toothandnail.com, this is a record company with many alternative Christian bands. Some suggested bands are: Flyleaf, Relient K, Officer Negative, MxPx (although they aren't a Christian Band but are "Christians in a Band" they do have songs reflecting their faith) Ace Troubleshooter, Flatfoot 56, Skillet, Paramore (another band of Christians, thought not technically a "Christian" band) or uniSEF etc. Take a look around myspace, there are tons of them.
All in all, this should help you be different, yet somewhat in style.

[edit] Tips

Don't be scary, offensive or dull in your attitude.
Don't overdo anything, like piercings and makeup
Do be respectful -- it's a kick to get respect in return...
Do jam with other Christ punks
Be moderate in all things

[edit] Warnings

People may "dis" you for your style
Christians may doubt your family's limits and/or intentions.
Some may consider your faith in complete opposition to punk ideals such as anti-authority and rebellion.
Understand that Jesus Christ was the one who apparently rebelled against the religious leaders of His day, and He calls His followers to rebel against the world and Satan by following in Him.
You may experience feelings that you're living a lie, since "punk's" core ethic is one of alienation, discontent, iconoclasm and individuality while Christianity emphasizes independence from posing (hypocrites), avoiding peer-pressure and overcoming irrationality through the victory in new-life and new-hope in Christ over despair in the world. Just read your Bible and these feelings may be moderated.