Engine sputtering

It takes a few pumps of the gas to get the car started. Once it gets started it "sputters" until I take off. It runs fine as the car is accelerating and maintaining speed. No stops or stalls. Once I get to a red light/ stop sign/ heavy traffic and come to a complete stop the car will slowly die. It doesn't happen all the time though, only occasionally. It just seems like its not getting enough fuel.

I'm thinking I need to change the fuel filter. Could it possibly be anything else? Like the carbuetor or fuel pump?

The most important question is: How do I change the fuel filter? Is there a free online diagram or a good website? I haven't browsed this site yet so maybe this is the one.