ease off to a run, face forward, crouch and steer with your knees. trim in main to close-reach angle.
Now move the tiller away from boom, while ducking and turning your back towards the new windward side as the boom comes over. shift sheet to fwd hand and tiller to aft hand. get your butt out onto the new rail, and QUICKLY midship your tiller and ease out the sheet a lot, soon as it tightens up on the new side.
Keep the bow downwind (or you'll round up and broach), no higher than a broad reach, and balance the boat out: if even keel, you're good. if heeling to leeward, ease sheet and bear off a little, hike out. if heeling to windward, do just the opposite. THe point is to keep "the boat under the mast", and avoid either the upwind broach or the downwind rejibe and death roll, with you on the wrong side and in the water on the latter event.
Once jibe's done and you're settled down, let off old jibsheet and bring in new one.
It's a balancing act, takes practice, but worth it.