Speed is your friend. Once you get your board speed, lock in your edge and push hard with your back leg. It is really important to maintain your board speed no matter what the wind is doing. If you are going fast you can go upwind.
Kite Low and Go. If you position your kite below 45degrees in the wind window, you can have better control of the kite by edging your board. When the kite is high, you get pulled off your edge and go down wind. With the kite low, you can edge hard, force the kite forward in the wind window and track upwind.
Stance is everything. Keep your back knee bent and your front leg straight. Dig your heels in so you are throwing a nice fan of spray off the tail of your board. Open your shoulders and hips in the direction that you are going, and most importantly LOOK UPWIND!
Some disagreement there...
1/ Speed should not be over-praised, enough speed to get going and keep going is ideal, more than that will not help a newbie go upwind.
2/ When the kite is lower than 45 degrees it is more likely that it will end up in the water in a bad moment, in which case any upwind ground gained will be lost in seconds. The upward force exerted by a kite higher than 45 degrees may act against edging but it is helpful to maintain planing as it counterbalances part of the rider's weight. A kite at 45 or a bit higher is probably the best goal for a newbie to learn upwind. Too high or too low does not help.
3/ As far as stance is concerned, is veeeeery important to push your hips forward and your shoulders backward, avoiding the toilet-seat stance, this is not mentioned in the article. Also, to stiffen your abdominals and your legs a bit by isometric contraction, in order to improve the transfer of power from the kite to the board, through your body.
Most of us know all these by experience but as the above - otherwise very helpful - article may now be read by many begginners, I felt there was a point in pointing out a few things