It all depends on which coin. Monero for example as it's own wallet. Any other erc-20 tokens (based on ethereum) could be used with MyEtherWallet.
it is token based, so do your research before sending any coin to different wallets.
Brother, you couldn't be more vague! I appreciate that you answered me but I'm sure allot of people out there could benefit from this question.
At what point do I make the link between my 'Market Buy' of say Ether (bought on Independent Reserve or any other exchange) and my wallet?
Do you send it there from the exchange you are using?
Do you make a request from your chosen wallet?
Do you copy the private key from your exchange and then past it into the wallet?
Maybe it is sent like an email?
It's a point I'm really lost on!