Open the rambutan by removing part of the skin in any one of several ways. Squeeze the rambutan till the skin breaks. Then peel half the skin off, leaving the other half to hold in your hand like a wrapper. Find a seam running down the top to the bottom of the fruit, and pull apart the leathery skin. You'll find something resembling a peeled grape, but larger, beneath it. Alternatively, use a knife to make an incision into the skin, and squeeze the fruit out. Do not cut through the seed.
Eat around the seed. Avoid biting too close to the seed--you want to avoid the tough, papery skin surrounding it. Some people nibble at the flesh, others pop the whole thing in their mouth and spit out the seed when they're done (see Warnings below). Some varieties have bitter seeds; others have sweet seeds, presumably containing negligible amounts of tannins or alkaloids. In the latter case, one can eat the entire fruit, seed and all (but not the outer skin).