I have done a lot of business at
https://localbitcoins.com/accounts/profile/BurtW/Are you buying or selling?
Buying:
Find a seller near you.
Open an order to buy BTC from them. I suggest an even amount of USD and let the BTC fall out of the price. That way the money is easier to count when you meet. For example buy $200 worth rather than 2.000 BTC worth.
The seller should then fund the contract. You will be notified when this is done. You will be given a secret number that only you know. Remember or write it down as it comes in handy later.
Arrange a place to meet. I usually meet at a public place with free WiFi, Starbuck's for example but any public spot (for safety) with free WiFi will do.
It is best to bring a smaller number of bills. For example if you are buying $5000 worth you should bring $100 bills, not $10 bills as it takes a long time to count that many bills. If you are buying only say $200 then it $20 bills work, etc.
The seller will then count the money and if it is all there they can release the BTC directly to your localbitcions account.
When the funds are released the seller will get the secret number that only you know. If he shows you that secret number then you know the BTC has been transferred to you. You can also just check your own localbitcoins wallet and see that the funds have arrived.
Most of the time the people I have met have been really cool Bitcoiners so if we have time we have some coffee and chat and get to know each other. Sometimes the other person is in a hurry or they don't want to chat for whatever reason and that is fine too.