Transferring Bitcoins from Wallet to Wallet Say I buy a Bitcoin from a specific market, like BTC-e, and it goes into my wallet. Is it possible for me to transfer that Bitcoin from its current wallet (BTC-e) into a wallet that I have on another market, like LocalBitcoins? If so, how can I do that and is there a fee?

Also, do all markets (BTC-e, LocalBitcoins, etc.) allow you to withdraw a Bitcoin from your wallet and exchange it for cash?
1) The exchange that has your bitcoin should have the option to withdraw bitcoins. It will then ask you to what bitcoin address you want to withdraw and how much.

2) The exchange you want to transfer the bitcoin to should have the option to deposit bitcoins, which will give you a bitcoin address to transfer to.

3) You can then directly withdraw your bitcoins to your deposit address.

4) Almost always these kinds of withdrawals and deposits are free except for the miner's fee, which will usually be BTC 0.0001.

5) No, exchange for cash is not always supported. I don't think a lot of exchanges would support this at all actually (unless by cash you also mean bank transfers?)