Comment: There are a few

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There are a few

ways to be anonymous on the Internet. The thing that identifies you is your IP address. So, to be anonymous you need to obscure the IP address you use to access the Internet.

You can do this by using anonymous proxy servers, or the Tor network. I actually like simply taking a laptop to a Starbucks or McDonalds, both of which offer free wi-fi.

Once you are on the Internet with an obscured IP address then see this for Bitcoin wallets:

http://bitcoinquickstart.com/how-do-i-store-bitcoins

Of course it's not necessary to be anonymous using bitcoins as they are not currently illegal.