Generally a tourist visa is issued by a US consulate abroad and good for a period between 3 to 6 months.
MOST IMPORTANT: You should file for the extension at least a month before your current I-94 (entry document) expires.
The best evidence you can provide of your intent to stay for a temporary period of time is a photocopy of a one way ticket to your home country after the proposed extension is approved.
Other evidence you should provide is a letter from an employer from your home country if you have a job waiting for you when you leave the US. If you have a lease/mortgage in your home country proof that you are still paying that monthly fee.
A bank account with substantial savings in your home country is also helpful.
In addition you need to explain why you want to stay in the US for a longer period of time i.e. want to visit other cities, friends. You also need to show that you are able to financially support yourself for the extended period of time. A letter from a friend in the US who will provide room and board will satisfy this requirement.