Hello Tabdog,
usually I try some kind of google image search first. Google is a wonderful tool, but isn't particularly smart. The secret is in asking the right question.
Searching single words like "token" or "freedom" or "eagle" will bring up a gazzillion hits that may not be related, however typing in token+freedom+eagle, meaning you are asking about all the words, narrows it down significantly. On the other hand, ometimes you can be too specific and not come up with anything.
It's all a matter of "asking" google the right question, plus a considerable amount of luck to come up with a good answer.
A google image search of token+freedom+eagle brings up this:
http://images.google.com/images?svnum=10&um=1&hl=en&q=freedom%2Beagle%2Btoken&btnG=Search+Images
BTW, the 7th hit on that page, looks like it might be a link to the manufacturer of your token:
http://www.hoffmanmint.com/tokens.html
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A good google trick is doing a site search. For that, just type in "site:web_address" and you will come up with pages showing the pics listed on the site. Like this: site:www.exonumia.com
http://images.google.com/images?svnum=10&um=1&hl=en&q=+site%3Awww.exonumia.com+&btnG=Search+Images
A site search can be narrowed down by adding search words after the address like this "site:web_address token" Like this site:www.exonumia.com token:
http://images.google.com/images?svnum=10&um=1&hl=en&q=+site%3Awww.exonumia.com+token&btnG=Search+Images
If that fails, there is always ebay, and a good catagory for many of the things we find like tokens and such is "exonumia"
I'd much rather use a google image search and quickly look through images for a match, than reading through pages of text, but when you can't easily find a picture, that may be the only alternative. Your eagle freedom token just happened to be one of the ones that came up first shot. Luck of the draw...