Fastest Way to Get Bitcoins
Once you find a seller who has a price you like with a good trust rating at a nearby bank, and click on [Buy]. Then enter the dollar amount and click [Send Trade Request]. At this point, the bitcoins you are buying are deducted from the Seller's account on Local Bitcoins and placed into Escrow for 4 hours.
You will see information or receive an e-mail with the sellers' name and account number at that bank. Once you have this, go to the bank with your cash. Get a deposit slip if needed and fill it out with the account number (some banks just have the teller take your account number verbally) and bring it to the teller. Tell the teller you want to deposit cash into the seller's account. Hold onto the receipt for the cash deposit from the teller as proof that you made the deposit in the unlikely case of any dispute.
Go back to your computer / phone and mark the transaction on Local Bitcoins as [Deposit Completed]. This will automatically notify the seller that you've completed your deposit. They will log onto their on-line banking website, and confirm that you made the deposit. Because the trader may be accepting multiple trades at the same round dollar amount, it is a best practice to add a few cents to the deposit so that it is a unique dollar amount and less likely to be confused with other depositor's deposit.
Note that you can only arrange these purchases when the bank is actually open, and that once you agree to a trade you need to go to the bank and deposit the cash ASAP, as your holding up this seller from selling their Bitcoin to someone else since it is being held in Escrow.