If you want to save money on installing your invisible dog fencing system, you're going to have to do it yourself. Professional installation cost is something that you're going to pay through the nose for. It's not a matter of finding someone who will do it, it's a matter of how much they're going to charge you to do it.
If you don't already have the equipment to run the line, however, you're going to either have to buy it or rent it. It can be done with one of two pieces of equipment: a trencher or an edger. In this case, the edger is the lower price alternative to use to install your invisible dog fence.
Edgers are more commonly owned by homeowners, so you could possibly borrow one from a neighbor. The problem with edgers is that you'll have to bury the line yourself by hand after the hole is created by it.
A trencher will make this a much easier process, because you can run the line and bury the cable at the same time. This makes the trencher a much better option, but you'll probably have to rent one because they're not a commonly owned item.
Of course, you could always go with the old hand edger method, but this is painful and takes way too long to be worth the effort. It will take a long time and by the time you're done, you'll wish you had spent the money to rent a trencher.