I was looking for instructions for how to build a tree swing and I found this wonderful tutorial:
HOW TO BUILD A ROPE SWING
It was straight forward and easy to follow.
A couple of things to remember. You will need more rope than you think you need. You will need extra length to help tie it off. We used about 60 feet of rope and our limb is about 20 feet in the air.
I found the board for the seat on the side of the road being thrown out by someone. Look around and see what you have.
I think we spent between $40-$45 on supplies. The rope added up, but it was really worth it! The kids love it.