IPhone 4 has frozen while updating to 7.1.2?

I started the update this morning about 2 hours ago and it has frozen while on the bit where it loads it up (it has like 1/5 of the white bar on it) I don't know what to do.

Basho has given a brilliant answer. The iPhone 4 is old and won't take on upgrades that will make it function better than it does.
I have the iPhone 4S and luckily it will get the iOS 8 update and it may just be its final update before I go for iPhone 6.
Please don't bother updating that iPhone 4 and enjoy it the way it is.
Cheers.

The iPhone 4 is an old iPhone. Each update is bad for the iPhone 4 because the updates are made for the newer phones released by Apple. Even iOS 7 was bad for the iPhone 4 and it contained watered down features of iOS 7 for the iPhone 4. Don't upgrade further than this but for now just wait and it will eventually start back on. IOS 8 fortunately is not available for the iPhone 4 because Apple does not create software for product older than 4 years so good for you. All you can possibly do is just wait. If you want iOS 8 than just get the iPhone 5 or above don't go for the 4s because that will not support iOS 9.

Love a tech savvy 13 yo

Please take your PORTABLE iPhone back to the store where you bought it. They will diagnose the problem, and fix it for you.

Did you read the part about connecting your iPhone to your PC via USB first, and "do not try to do the update WIRELESSLY"?

Also, I do hope you did a Back Up to iCloud recently. They may be forced to return your iPhone to Factory-new condition, which will wipe out all of your personal data files, videos, notes, photos, etc.

My iphone 4 doesn't charging, what can I do

Call Elsa and ask her to fix it.