One of the best ways to buy old records is at a local vintage store. The stores are often owned by music enthusiasts who are knowledgeable about vintage music. For example, if you're a Miles Davis fan, the store owner may be able to tell all about the jazz legend's life and career and offer rare vinyl albums of his music.
A local flea market is a really good way to find old music. For example, if you were looking for the Beatles' "Abbey Road" album, one of the merchants may have that same album and probably at a lower cost than the bigger music stores. Some merchants may even have musical biographies, which help you understand the music better.
Sometimes you don't have to look far to get old music records--your family might have some. For example, you may be a Stevie Wonder fan but prefer his music from the 1970s rather than his later albums. If your parents have some of those albums, you can see about getting the albums from them. They also may have stories behind why they enjoy his music.
Another way to get rare or out-of-print music is to shop online stores. For example, www.alibris.com is a site that specializes in this genre of music. Other good websites to try are www.rhino.com and www.ebay.com.
When purchasing vintage records online, make sure you deal with a reputable website. Millions of music sites exist, and some of them could be scams that seek to take your money. Before buying from a site, visit the Better Business Bureau's website, www.bbb.org, and see if the company is legitimate.