I had a pipe rupture just inside the foundation of my house last year. It was a 1/2" copper pipe and it froze.
I didn't know how to sweat pipes, didn't have the tools, and the plumbers in the area were all swamped with cold weather repairs.
I went to the home improvement store, and purchased a compression union. A compression union is a brass piece that you can use to splice in sections of copper and steel pipe.
The union has a center section which acts as a coupling. Each each end has a fitting and a spherical ball piece with a hole through it.
To use a compression union, you cut your pipe and clean it. Then you slide the end cap onto the pipe, slide the compression ball onto the pipe, and stick the pipe into the center section as far as it will go. You simply tighten the end cap with a wrench, while holding the center section fixed. Repeat steps for the other end.
Buy two fittings, cut your new pipe to fit, and union in a new piece. I was told that it may eventually start leaking. I made this repair over a year ago, and it hasn't begun to seep yet.
If you're on a budget, no special tools are needed. I think it may begin to leak because the copper is soft and takes a set. If so, you can cut out the piece with the two unions and repeat again until you can afford to fix it properly.