Currently, I prepare onions to put on a pizza by using a food processor to chop them, then strain them and let them dry. Then, I put them in containers before use.
However, the onions have been too moist lately, and make the pizzas soggy when they're put on them. How can I remove some of the moisture so they don't do that?
One technique for removing water from a vegetable, which works very well for onions, is to salt them liberally. Then give them some time to sit, preferably in a shallow layer.
The salt will extract water from the vegetable, due to the osmotic gradient between the salt outside and the vegetable inside. Some of the salt will go into the vegetable, but much will remain outside; you'll need to figure out how much salt you can get away with using before your vegetable is too salty, but it's typically a large amount in my experience.
Once enough water has been extracted, rinse the vegetable off (to remove the excess salt), and pat it dry between two parts of a towel (or two paper towels). The vegetable will now have much less moisture in it, which will both lead to crispier and quicker frying, and less moisture coming out in the cooking process.
A second option, in your specific case, is to store them in open containers. The refrigerator will dry the onions out over time. This is usually a bad thing, and you intentionally close containers to prevent this; but in your case, depending on the length of time you're talking about, it could be a good thing. I wouldn't do this for more than a few days (as it will really dry the onion), but it might be worth testing to see if it helps. This may leave your refrigerator (and its contents) smelling like onions, of course.
Alternately, you can store the onion on a mesh or grate which allows moisture to slip down below the onion; it may help prevent some moisture re-absorption and improve your results.
Or you could try saute em before hand then just drop em on few minutes before your pizza is done?
You could, of course, actively dry them, in a food dehydrator or one of the many improvised versions of the same thing. You don't need to completely dehydrate them (unless, as @mrog does, you find that you like that) though if you do you can skip refrigeration. I often partially dry apples when making apple pie to get the "pie juice" thicker without resorting to corn starch or tapioca. I also mix fully dried apples with normal apples. I see no reason that the same techniques should not apply to onions and pizzas.
That would be easier with sliced rings rather than diced/chopped onion, which will tend to clump and probably be difficult to dry. I guess mixing purchased dried onion or garlic with the diced/chopped onion might work, if rings are not an option.
