Can I put my iPhone sim card into another iPhone?

I have an iPhone 4 but I want the 5c. Can I put my sim card into the 5c and it work?

Yes and no, your iphone 4 uses a microsimcard and the iphone 5c uses a nanosimcard. The difference is that the nanosimcard is smaller than the other. You could however clip the microsimcard to the size of a nanosimcard. There are lots of guides on the internet on how to do it.