If you're making a standard brew (ie not high alcohol, <1.06)...
Add 1 cup DME (and 1/2 tsp of yeast nutrient, if you have it) to 1 liter of water and boil for 10 minutes. Transfer to a sanitized 2L or greater flask, bottle, or container, let cool to ~80F and pitch yeast (for pitching into 1L you should have the equivalent of a wyeast propagator pack in yeast...if not, see below). Cover top with aluminum foil immediately after transfer to keep out the nasties--do not use your airlock! If you are VERY paranoid about nasties you can also stuff the neck with cotton wool and then foil (like in vitamin bottles) but aluminum foil should be fine.
There seems to be a lot of argument about whether or not to airlock the starter--the point of a starter is to get your yeast to reproduce like crazy to increase your pitching rate. Yeast reproduce much better in the presence of oxygen (this is why we aerate the wort) so the starter should not be airlocked. This is also why it is important to use a container much larger than the volume of your starter...more oxygen!
Place covered starter in a warm spot (~80F) and grow for 24 hours, swirling as often as possible to resuspend the yeast (or use a stir plate). When you're a few hours away from pitching, don't swirl and let the yeast settle. That way you can pour off the presumably nasty tasting oxidized wort and pitch only the bottom 1/3 or so of your starter.
IF you're starting with a freezer stock or fewer cells than a propagator pack....
you need to do a serial starter. Using the above procedure, do a 10 mL starter overnight and then pitch this entire culture into your 1L the following day. If you pitch a small number of yeast into a large starter, they will not be as healthy and you will be more likely to get contamination since the yeast will not be able to multiply as fast and outcompete the nasties that survived sanitation.
IF you're brewing a high OG brew....
You'll need a 2L starter since more alcohol means more stress for the yeast! Start with the 1L for ~24 hours, let it settle a bit, decant, and then pitch into 2L. Also consider repitching yeast when you rack to the secondary.
hope that helps!
Cheers.