Can a SIM card from my htc one v fit in an iPhone 4?

My current phone is really crappy and I wanted to get a new phone without getting a new plan

Yes just use caution and do some research before opening the iPhone 4, or have a professional do it for you.

You'd have to cut it to microSIM size.

http://www.iphonehacks.com/2010/06/how-to-convert-a-mini-sim-into-a-micro-sim-for-iphone-4.html