Most philatelic publications like to run repeated stories about great rarities and how they came to light. Face it - you'll never find a rarity. But on a more practical level where can you find stamps that aren't new issues - widely marketed and available to all - which may have been sitting around unexamined for years?
The answer is simple: in old stamp albums. But where do you find "unpicked" (i.e. the more valuable stamps haven't been pulled out, leaving the common stuff, which you may already have) albums that can yield real value? Older stamp collectors, of course. One of the beauties of the hobby of stamp collecting is that are always willing buyers of your items if what you have collected is up to their standards and the price is right.
Most who sell their collections sell them to dealers, who are in constant need of new material for their customers. Most independent stamp dealers will offer old albums containing a sampling of stamps and usually there will be a few good ones left to get your attention. But be assured that the best stuff is already stripped out and stamps once in the album will be sold individually or in small lots. This is the way the dealer makes his profit on the album he bought from a collector, not by selling a partially filled album containing more common stamps.
Beat the Dealer to the Stamp Collection
So your job is to find the collectors ready to sell before they take their albums to the dealer. If you want to be serious about your search you might take an ad out in one of the philatelic publications (though taking out an ad in an online source would be more practical) letting collectors know that you will beat any dealer offer by a percentage of your choice. You're relatively safe, because dealer offers are traditionally so low that even if you have to pay ten or fifteen percent more you'll come out ahead.
Finding Stamp Collectors Who Want to Sell
Go to stamp club meetings. You should be doing this already for many reasons, least of which is to buy stamps from other collectors. Ease your way in -- you don't want to be perceived as some interloper or opportunist. After all, you want the stamps for your collection, not to simply realize a quick profit.
Go to stamp collector's chat rooms - again, you should be going to these already as part of the enjoyment of the hobby. There is always much to learn from other collectors. But be sure that it is not a chat room run by a dealer. If you ask other collectors about buying their collections in such a venue you might get the boot from the host, who is probably interested in the same thing you are: buying stamp collections from collectors.
Don't forget one of the oldest ways of finding collectors who want to sell - by reading classified ads in the philatelic press. From the earliest stamp club newsletters of the 1800's collections have been offered for sale. Although now most notice of sales are posted online, the back pages of stamp journals and newspapers can also be a source for contacting other collectors. Consider buying such an ad - they are inexpensive, and while print media is having a tough go of it in many areas, stamp collectors are still reading anything that may reveal a good find.
If you are a new collector looking to buy an existing album of stamps be aware that dealers not only have these partially filled albums, but also mass produced items you might want to avoid. Collections of gold replica stamps, modern takes on classic advertising covers, themed collections (Bicentennial, flags, aviation milestones, etc.) that collectors have dumped for pennies on the dollar are often available. While these items may be fun and simple to collect - they are subscription items and the collector doesn't have to lift a finger to accumulate the items in this sort of "collection." As such they are a great example of how your collection, that you personally put together piece by piece and with care has a much greater value than the instant heirloom collections.