I have a 99 Escort that has a big leak from one of the transmission lines (leaves a trail). A mechanic has quoted ~$200 to replace the lines.

If I wanted to replace them myself, what would be involved?

It's not that hard of a job swappin trany lines , everything is available at your local parts store. Just make sure you have the car supported very well if you have to raise it off the ground (ie good quality jackstands!!!) As far as special tools you should use fitting wrenchs'and possibly a tubing cutter.