That's called Mail Merge.
The key thing with Mail Merge is that the data to be merged must be broken into fields. The typical address label usually has three or four pieces of the name, a street address, possibly a second line of street address, a city, state and ZIP (in the US, province and postal code in Canada). If you're using Access, you most likely have these already. Excel users are more likely to clump some things, such as the pieces of the name, together into a single column.
Each data field can then be positioned for printing any number of times on the merge document using data fields. Another field ({NextRec}, I think) advances to the next data record on the database.
Far too much to go through here, so I'll just give a few tips:
1. Word's Mail Merge can be found in the Tools->Letters and Mailings menu item in early versions of Word, or on the Mailings tab on the ribbon in Word 2007.
2. Note that a Mail Merge run does not have to print the entire mailing list. You can have it print on the basis of the data, say, ZIP code, or for a single address whose label was mangled.
3. Before wasting pages of labels, run tests on regular paper and hold the sheets up against the labels to check the layout.
4. Don't leave the setting up to the last minute. Mail Merge can be frustrating and take more time to set up than one would think.
5. For test runs, use only enough names to be sure you're not losing any -- a little over a page should do. Accidentally skipping every other name is real easy to do.
Keep a sense of humor while you're wrestling with it. It will be worth it the second time around.