Supposed training of Misha here.
Gelnn Pendlay on the push press:
My advice on push press is to #1 get your squat and front squat up. That's a whole other thread, but it's safe to say that you wont be push pressing 300lbs with the same squat numbers that you are push pressing 230lbs with. You'll need strong legs.
When I push pressed 440lbs, I had done 770 for a triple on the Olympic style squat wearing only a belt, and 606lbs for a set of 10 without even wearing a belt. Rob McAdams push pressed 375lbs weighing about 200lbs, he squatted 400lbs for a set of 20 OL style with no belt, and did front squats with 440lbs and more wearing only a belt. It's hard for me to imagine a 300lb push press with much less than a 500lb OL style squat done raw. I'm sure its been done by some freak, hell some freak out there probably push presses his max squat. But if you're aiming for 300lbs on the push press, I'd aim for 500lbs on a raw squat done deep and a stance close to what you are push pressing with.
Now as to training the push press itself... I would do them twice per week if you are no good at them, if your technique is bad. Do this just to learn the movement. If you are skilled at them, cut it back to once. But do overhead work 3 times per week if you can. Do a variety of movements. Military press, push jerks, even snatch grip push press, and regular push press with the bar behind the neck. Benching once per week won't hurt you, but if you bench too much, it cuts down on what you can do overhead, at least in my opinion.
A good workout emphasizing the push press might look like this
5x5 on military press
3x5 on push press
3x5 on bench press
3x5 a little lighter on some other overhead movement, like push jerk, or snatch grip push press
Start conservative, build and after 4 or 5 weeks change the reps or one of the exercises.
For variety, you can do complex exercises... for instance, on one of the days, you can use a weight you can do around 4 or 5 reps on the military press, press it for 3 reps then push press it for 3 more, for 3 or 4 sets.
Or, if you know how to jerk, take a weight you can push press say 5 times, push press it for 3, then jerk it for 2 or 3 more... again for 3 or 4 sets.
These complexes are killers! Don't overdo them.
That's basically it, get your squat up, and practice overhead work. Its nice to see someone interested in my favorite upper body exercise. A big bench is cool, but there is always the equipment controversy. A big jerk is simply a thing of beauty to me, but there are always those who scream "it's all technique" and dismiss the strength needed to do it. But a big push press, I don't know, to me, its just the absolute coolest expression of shoulder/arm strength there is. I think a big push press is a damn cool thing.
Just remember that the real "meat" of a program isn't so much the exercises or the days of the week... it's how you plan/approach your progression. Make sure you keep good track of what your doing... try to make small steady jumps on your weights, try to do things in some sort of systematic way and not be jumping all over the place. And last, listen to your own body, use your own head! Listening to others is good, but if you listen TOO MUCH, and don't think for yourself, you'll end up flying all over the place always trying the latest greatest thing. Pay attention to what is working for you, and what isn't. Make changes in a reasonable fashion, know why you are changing, and change one thing at a time so you can monitor the results.