I wouldn't suggest ever "squeezing" the water out of a pad. You can usually fling most of it out just by making the motion like you are going to throw it on the ground. Its hard to describe the motion, but you can figure it out. Just shake it with as much power in one swing as you can without spraying water all over the place. Usually just raise it above your head and swing your arm down hard will force most of the water out. Then put it back on the PC and spin the rest out on a low setting. Remember to put your hand in front of the pad so the water doesn't spread everywhere. Likely it will be milky and will leave marks everywhere.
You can use the pad wet for a number of different products. Polishes work best if the pad is dry, but a damp pad doesn't really hinder it too much. It just waters down the polish and limits effectiveness. That is why it is good to get it as dry as possible. It would be best to have two pads so one could be out sitting in the sun while you use another one. Then when you need to clean one the other one might be dry enough.
Some products like AIO work best with a wet pad, so its just not always a bad thing to have it be a little damp. Just sling as much water out as you can before going back to work and you should be fine. Start looking at getting a backup pad if you find that you have to clean your pad out a lot or are using it alot.