The answer is not very well. You truly get what you pay for - a cheap burr grinder is never a bargain. Unless you happen to stumble across a used sem-commercial burr grinder (Anfim, Cunill, Rancilio, Mazzer etc) for a dirt cheap price... which is unlikely... the least expensive burr grinder worth buying will be a Starbucks Barista or the Solis Maestro "Classic" (same machine as the Barista).
What you probably want is a burr grinder. These provide a more uniform grind with little to no dust. They are more expensive, of course, but definitely worth it. Recently I have been seeing more of these and the prices are much lower ($20-$50 at Costco, Target, etc…) than I used to find a couple of years ago ($150+). However, I am not sure how well these lower cost grinders work...
Cheap burr grinders produce an inconsistent particle size, tend to run very hot (heat is bad for the beans) and rarely do a better job than one can do with a whirly blade grinder. The trick of pulsing the blade grinder and also shaking it a few times between pulses will help to produce a reasonable consistency in particle size but the only way to get really good uniformity is with a grinder of the proper quality level.
That's an important point. The SCAA (American) standard is a six ounce "cup" per standard coffee scoop (which should be roughly 7 grams of coffee) but Bodum dictates a four ounce "cup" for their press pots and vacuum pots.
I use one of the scoop that came with the Bodum grinder per 4 ounces of water.