Lilacs need sun to bloom. If they don't get it, you'll have a weedy looking plant that you'll curse forever.
I've never transplanted lilac seedlings, but I would imagine it's just like transplanting any other young plant....big hole, lots of nice, rich, new dirt and lots of water to get those roots feeling loved and at home.
You probably won't see flowers for a few years. Your lilac will probably put all of its strength into growing and spreading roots. So don't dispair if it takes awhile!