Yes, there are a couple of ways to do this.
If you are shooting in a mode like Program mode, Aperture or Shutter specific mode, your camera will determine the exposure based on how your have your metering set up.
Matrix metering = Takes the whole scene into account and sorta creates an acceptable exposure. Usually best in uniformly lit-scenes, but can give bad reading in contasty situations.
Spot and/or Center-weighed: Takes one specific area of the scene to draw it's exposure calculation from. Spot is a very precise measurement, while center-weighed does pretty much what it says it does. Wider radius of exposure determination based on the center of the image.
So, often times you find yourself in situations, like a portrait against a dark background, where you want to meter for your subject and not the whole scene, but you don't necessarily want to plop them in the center of the scene either.
Most DSLRs have a form of Exposure-Lock. I know it's called AE-L on Nikons, not sure on other manufacturers. That will let you meter where you want to, press the button, and maintain that exposure information while you re-compose. There is usually an Autofocus Lock function as well if you are curious.
The other way to go about it is just to shoot in Manual mode. Use spot or center, adjust your exposure with your Aperture/Shutter speed until you get something acceptable, then recompose and fire.
Ultimately, using something Auto-exposure lock is great when you are trying to get a quick shot correct or don't have the time to sit and really compose.
If you have the liberty to take your time with the shot, using manual mode will help you fine tune to just the right exposure you want, and will also help you become more familiar with the basic functions of your camera.
The light meter can be a great thing, but it just isn't always right, so shoot and tweak until you get it right, then remember the settings for next time!
Hardware: Nikon D80, Sigma 10-20mm, Nikon 18-55 mm VR, 55-200 mm VR, 105mm f/2.8D Micro, 35mm f/1.8G, SB-600, Manfrotto/Bogen 190CXPRO3 + 468MGRC2
Software: Aperture, Photomatix, GIMP
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