yeah for tools i'd find a 12" cresent wrench and maybe a set of channel locks (some people call them pump pliers)
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Lemonie has it right for the handles.
The water inlets will be held on with compression fittings, and the faucet will be held to the sink basin with large (3/4-1,1/2 inch) nuts. Get a wrench large enough to grip the largest nut you can find on the underside of the faucet. (adjustable wrenches are good for this)
The new faucet will come with instructions of what to hook up where. Ask at the store - most hardware stores will give you a visual walkthrough of hooking up the new supply lines, holding the faucet down, and testing for leaks.
Can you see a screw anywhere? If not there will probably be some kind of cap on the top which will prise off with a knife. Expose the screw, remove it, take the handle off.
Take a picture and post it here