Bitcoin Forum

Like the title says.  I did search but couldn't find an answer.

https://en.bitcoin.it/wiki/Getting_started#Getting_my_first_coins

So if someone sends me BTC when my computer's off.   I switch on a few hours later and fire up bitcoin - the transaction should be showing straight away?

No - you would have to wait until your client updates the blockchain before you see the transaction appear.  It wouldn't take long if your computer was only off for a few hours - a matter of seconds, really.

If you have your Bitcoin client open at the same time the transaction is sent, you should immediately see that someone has sent you money. However, in order for the payment to be processed, the transaction needs to be included in the Bitcoin blockchain, which can be a few minutes to a half hour. Waiting several more Bitcoin blocks after the one that contains your payment ensures that the payment to you will be a permanent addition to the blockchain, and the Bitcoin client considers six more blocks (about an hour) as when the payment to you is "confirmed". Your Bitcoin client also needs to have downloaded all transaction blocks including the one with your payment to see these confirmations.

You can always see the status of a transaction using a real-time blockchain explorer utility, such as:
  http://www.blockchain.info (http://www.blockchain.info)

Simply enter the receiving address into the search field.