Ohhh! Yay for sergers! What model did you get?
Most of the garb I make gets serged on all sides (unless the edge is going to be concealed in a facing) before I start construction. It takes a bit longer, but it really helps extend the life of the garment and makes it look really nice inside and out.
If you serge the edges first, make your seam allowance a bit smaller.
If you don't want to pre-serge everything, you can serge both raw edges together after you've finished construction, before you press your seams open. This is the method most commonly used on store-bought stuff, but it doesn't leave any room for alterations if you're making garb for someone else. Press and/or topstitch the serged edges to one side.
You can serge some seams together (as opposed to serging THEN sewing them), but you don't want to do this to any seam that will have any strain put on it (shoulder seams, side seams). On a tunic, I would limit it to a back seam if you have one, and maybe the sleeve seams.
You can use a serger on parts of your gambeson, but for the most part, you're going to want to do most of the construction with your sewing machine. I would use the serger to tidy up any raw edges that might be left over on the inside.
Sergers also make hems really easy and fast! Serge the raw edge of your hem, press it up about 3/8-1/2", and stitch down!
Fold-over waistbands are easy, too. For drawstring waistbands, put your drawstring holes in first, press in half with right sides out, pin to garment and serge. Elastic is a bit trickier, but you can sew the elastic together, insert it into the folded over waistband and serge it to the garment.
My serger gets almost as much use as my sewing machine. These are just some of the tricks that I use on a daily basis. A lot of people think sergers replace sewing machines- they're supplements to sewing machines. When I first got mine I did most of my actual construction on it, but it doesn't hold up as well as using it to just finish the edges and take little shortcuts here and there.
Good luck!!
Kevat
BadAss Garb
http://www.badassgarb.com