I play Alto Saxophone, and I've been wondering this for quite a while now. I've not played one single overtone yet, so what are your suggestions?
Edit: my use of the word "embouchure" is apparently not in accordance to the common meaning. See comments below. You should perhaps mentally replace all instances of the word embouchure with something like "shape of oral cavity". Apologies and thanks to NReilingh for pointing it out.
For practicing overtones, first you need to get your embouchure used to the overtones. A simple way of doing it is to finger the higher register, start blowing, and letting go of the octave key. Repeat it several times until you can play the higher note from the attack, without using the octave key. Once you get the first one down, the rest will follow easier.
As far as I know, overtone practice is a way to train you embouchure. When practicing (again, in the first few times you may have to repeat step 1 to regain muscle memory) try to attack the lower register note and shift to the overtone without tonguing or in anyway stopping the airflow. You likely won't be able to do it at first, but it will come with practice.
To practice the second overtone, one trick that my teacher taught was to play the actual note (say, the high D). Then hold your embouchure, finger the base note (in this case low G), and blow. In the beginning you will only be able to hit it once every few times, but with practice you will get better control.
After you can get the second overtone on attack, you should repeat the exercise of jumping between overtones without interrupting airflow, but now jumping between the fundamental, the first, and the second overtones.
(Part of the production of overtones depends on your horn and its tuning. On my alto it is easier actually to hit the third overtone for low D [high D] then the second [middle A]; while for everything else lower than low E the second overtone is easier.)
Something to keep in mind when you practice overtones is that the embouchure shouldn't really change, but the position of the tongue in your mouth will change significantly (pay attention, for example, to how your tongue moves in your mouth when you whistle an octave).
A common mistake is to tighten you mouth on the mouthpiece harder when playing overtones, but you need to resist that temptation, and find what works for you (I tend to think of an "ah" kind of sound to keep a round mouth). The warmup exercise I use often is to play a low Bb, then, without moving the fingers, play a middle-of-the-staff Bb, then a top-line F (all can be played with the low Bb fingering). Then I do the same thing with B-B-F#, then C-C-G, C#-C#-G#, and D-D-A. The second time through (or once you master those overtones), add the 3rd octave to the series (e.g. Bb-bb-F-Bb). You can stretch it out at least another few overtones, but those exercises are a good start and they are useful for other aspects of your technique as well.
If you find it difficult to get the higher overtones, try playing you low Bb fingering with the octave key, then lift the octave key and try to keep the same sound. After you have the hang of playing overtones, try playing with different dynamics or going up the scale (e.i. low Bb, mid Bb, low C, mid C, low D, mid D, etc.)
Overtones do very much depend on your setup, especially your neck and your mouthpiece, but also your sax body itself.
Alan's tips (the last paragraph) are very good. You can also practice your overtones with just the neck and mouthpiece, this allows you to get more control over your overtones. Again, how easy they are to create very much depends on your neck. This is the reason aftermarket necks and mouthpieces do exist. They do make a difference.
My secret trick is looking up. Your mouth will automatically readjust your tongue (wheter you'd want it or not) and you will have an easier time to produce overtones.
Literally just look to the roof while trying to play overtones.