Make sure the horn is in good shape. It's hard to play with good tone through leaks.
Check reeds. Chipped, warped, cracked reeds won't play well. Make sure their reeds are lined up properly.
Many band directors (and young sax players) seem to think that a stronger reed is always better. I see kids all the time playing on #4 reeds and they can't play well at all. At first, students definitely progress up from softer to harder reeds, but after a year or so they should settle in. At that point it's a matter of matching the reed to the mouthpiece. Most of my HS kids are playing on a 3.5 for concert band. Some are on a more open mouthpiece and playing a 3. Very few people sound good on a #4 reed, or anything less than a 3 (for a concert band mouthpiece). Jazz mouthpieces generally have a wider tip and need softer reeds.
I'll assume you have a good knowledge of basic saxophone embouchure and you've checked that.
The most important thing for saxophone is checking their mouthpiece pitch. Most high school students are playing with their embouchure far too tight. Have them play their mouthpiece to a tuner and see what note they get. Goal notes should be concert pitch A (alto), G (tenor) or F (bari). Most kids will be a step or two above that. To bring the pitch down, they need to lower their jaw and firm their corners. In saxophone sectional we do lots of exercises with sirens to get them flexible, then shoot for that concert A. Once they get the right pitch on the mouthpiece, they have to keep that same embouchure pressure as they play the full saxophone. Biting the reed leads to weak, pinched tone and poor intonation.
Next work on air. Saxophone should be played with an open throat and oral cavity. Tell them to think "ah" shape in the mouth, or imagine they've just eaten something far too hot and it's sitting on their tongue. They should think of warm air (fogging a mirror) not cold air (that's for clarinet).
Check posture. Too many sax players have bad posture either because they want to be "jazzy" or they're just lazy. Of course they should be sitting up straight with feet flat on the floor, like everyone else. Make sure they are holding the saxophone so the body is pretty close to vertical as you look from the side. Horn angling across the body is fine, but don't let them put the bow on their knee or have their right hand back by their hip. Make sure they adjust the neck and mouthpiece angle so the mouthpiece goes straight into their mouth, they should not be contorting their neck to reach.
Those things will take care of most of your problems. You can start working on matching octaves - play low G, then high G, make them sound the same. Work on matching registers - go from B in the staff up chromatically to D in the staff - try to make all of those sound the same. If you use the blue Foundations book, look at the warmup exercises option 2. Overtone exercises are great, but need good supervision to make sure they're not just biting the reed (check out "Top Tones for Saxophone" by Rascher). Long tones and chorales are good for everybody.