All Localcoin transactions happen immediately, so you should receive your bitcoins right away, provided you sent them to the correct address. If  you have confirmed, with 100% certainty, that you sent them to the correct address, you most likely just need to close out of your wallet app, then reopen it.

Some wallets will not show your bitcoins until the transaction has been confirmed on the blockchain (not to be confused with the Blockchain wallet, which is named after the blockchain). This usually takes about 10 minutes, at minimum, depending on the state of the network.

If you are concerned that your bitcoins haven't been sent, you can check the status of your transaction by going to (a blockchain explorer) and searching for it by inputting your wallet's address.