Is it cloth or something other? Glue the front first, pull tight to the back and use a putty knife to tuck it into the slot above the door frams. Good staple gun is a must, use short staples and make sure the tack strip is clean and well anchored. Go slow and keep working the wrinkles out of it.
$100 is what they charge over here also. It'll be well worth it to pay this especially since you've never done one before. Even doing it your self it'll cost you about $30 or more just to buy the headliner. Chances are you will screw it up, trust me I've done exactly that before. No real savings here.