I've actually just done a transaction on there as a Bitcoin buyer so I'll explain the process from that perspective.

1. I sent a request to an advertisement offering to sell Bitcoins.
2. I was presented with (in this case) the UK bank account payment details.
3. I sent the payment via my online bank account.
4. I clicked a button on the Local Bitcoins site to say that I have paid the invoice.
5. The seller released the bitcoins from escrow.

I believe, although I am not certain, that the bitcoins are put into escrow as soon as I sent the request to the advertisement (so step 1.5). I've not yet seen this process from the seller's perspective.

Unfortunately, I am not certain first-hand how this process works if you are transferring via cash in hand. There are more details on the 'transaction service' that offer which is designed for cash in hand - see the link below.

https://localbitcoins.com/faq#howto_why_transaction