You receive bitcoins in the form of transactions. Once a transaction has been confirmed (put into the bitcoin blockchain) it is valid, and you did in fact receive the amount of bitcoin transferred in the transaction.
As a security precaution, for higher amounts you should wait for a number of confirmations (additional blocks built upon the block in which the original transaction was recorded.) A typical confirmation count is 6, although that is pretty arbitrary, 3 would be pretty safe in the current blockchain environment.
If you want to check whether someone actually has the bitcoins they offer you for a trade, you can let them sign a message using the bitcoin address with the balance.
As an example of such a signed message, here is one that I signed using my signature address:
Address:
1HvaoWCtvG2pvd8B9nvr9DjiErnSmjCqAY
Message:
I don't want to buy gold.
Signature:
HBxJ6x/QwG4W8a+uCwtMt56f9AaXzMOP/pJdyUNxBskKN0rG4WqjzpIH2992nZl/C4BImeZ/t2AcQgJWMPobTxM=
(you can verify the message at
https://coining.com, and you can check the current balance at
https://blockchain.info/address/1HvaoWCtvG2pvd8B9nvr9DjiErnSmjCqAY?sort=0 so if I proposed to buy gold from you you'd know that I don't have enough bitcoins at this address for an ounce of gold)
Directly exchanging bitcoin for gold and vice versa is probably not very efficient, as there are few companies offering this service, so they can charge a premium for it due to missing competition. Trading with private (possibly anonymous) persons is pretty risky, especially when buying gold with bitcoins, as verifying the gold is much harder technically than verifying a bitcoin transaction. You also need to consider that you risk getting mugged, or if you want to do the trade due to legal reasons (India comes to mind) that you might get caught in a law enforcement sting operation.
Onkel Paul