I brew German lagers quite frequently because Oktoberfest/Marzen is my favorite beer style to sit around and drink. I have a 1000ml flask that I make my starters in. I usually step it up twice. And I do not have a stir plate. I just swirl it several times when I pitch the yeast the first time.
Each time I boil two cups of water and a half cup of extra light dry malt extract for about 10 mins. Chill, then pitch my yeast. I like White Labs German Lager yeast in particular, but everyone has their favorites. I then attach a stopper and airlock and it's usually done working in a day and settles out in a day. I then pour off the liquid that sits above the yeast, and repeat. Two steps should give you about 400-500 ml of yeast.
I start this about 3-4 days before I want to brew. After the second step I just pitch that into the worth that I brew. There are many different strategies on lagering, but I let the wort kick off nicely before I put it into the fridge. And then I put it in at 65 and gradually reduce the temp until it hits about 55.
Be sure and not reduce the temp too fast otherwise you may shock the yeast.