This clip of Kerstin Reiger from continentseven illustrates the key points.
The very first thing she does is move her back hand down the boom. This is really important and easy to miss so make sure you catch it. Why does moving her back hand further back matter? Shifting the hands back is tantamount to shifting the sail forward, which as we know makes the board turn downwind. Shifting even just the back hand initiates her downwind turn.
Next she makes a (sudden) move to get out of the footstraps. But note that she ends up further back on her board. Shifting her feet and hence her weight back helps turn or pivot the board around its back.
Once she is sailing downwind ("running") she switches her feet. Then she continues turning for awhile and finally she flips the rig. ("Flipping the rig" is an expression for flipping the sail.) Watch her front hand just before she flips -- it slides right next to the mast. Sliding the hand to the mast is a common prelude to any rig flipping maneuver and it sometimes goes by the name of a boomshaka, a neologism coined by Guy Cribb. Do a boomshaka before you flip your rig.
Again, pay attention to the feet. They are back when she's running or nearly running. In the middle of the jibe this helps resist the force of the sail. But then notice how her feet shift forward again (closer to the mast) just before she flips the rig. If you are too far away from the mast when you flip the rig, it will pivot far away from your body, whence the sail will be imbalanced and end up falling into the water.
When should you flip the rig? Wait until after you've switched your feet, i.e. after passing 6 o'clock. (You should be sailing on a "broad reach.") You can even experiment by choosing not to flip the rig at all! In this case you'll find yourself sailing clew first, which is a handy skill in its own right. Try it: Don't flip the rig yet. Turn a tad more upwind than she does and sail clew first for awhile. Then, at your leisure, flip the rig. Remember the boomshaka: Slide your hand to the mast before flipping.
By the way, did you watch her knees? They're bent, as they should be, but not by much. She doesn't need to because the wind is not too strong. But bending your knees will stabilize and improve your downwind sailing.
For a good example of bent knees, watch Jem Hall's gybe from his website.
He's also demonstrating other lightwind jibing points discussed above:
That means that he sails comfortably clew first -- note how high he raises the clew and how near the clew his his old back (right) hand is. As in the first video above he shifted his back hand early back toward the clew. He then waits until he's sailing in the new direction (nearly 9 o'clock in his case) before flipping the rig, as always, with the help of the boomshaka. He does a nice rig flip, no?
His jibe also illustrates the sweet spot: Note how the board seems to turn by pivoting under his rear foot. That happens if you move your weight back far enough. Move back to locate the board's pivoting sweet spot.
ABK Boardsports advocates straight legs when sailing and even when jibing. The rationale goes like this: straight legs provide a solid connection and efficient transmission between your body and board. Moreover, straight legs, like straight arms, are less tiring on the leg (or arm) muscles, since you're relying more on the structural support of your skeleton. And indeed you'll see many top competitive windsurfers sailing on a reach with one or both legs straight. However, straight leg(s) during a jibe are uncommon. That said, as with every element of windsurfing it behooves you to experiment and discover for yourself what works best.
There are lots of other kinds of jibes. Here are 3 of them: