Lilacs are shrubs and not trees although they can grow easily to 15-20 feet. It is a shame they were allowed to get so large. You are going to have to prune aggressively taking all that old growth out over the course of three years or so.
Chris' reference is great. There was a great little book published ages ago called, "How to Prune Almost Everything" but it is out of print. You can find a used copy I am sure. It is one of the best books I have ever found on pruning basics. There are no doubt lilac specific books at the library.
You might want to read up on layering as a method of plant reproduction. It works well with lilacs. Essentially you peel the outer bark away from a section of healthy branch and wrap the wound with spanghum moss and plastic. In time roots will form and you have good healthy stock for starting a new plant identical to the one you may be losing.