Deep tissue massage should feel like a "good hurt". If it's bringing tears to your eyes and making you want to bite the sheet, it's too deep. Your muscles are going to guard and the massage will not serve its purpose. On a scale of one to ten, it really shouldn't be any more intense than a six or a seven. If it's too much, you need to let the therapist know so they can back off a little. The only way they're going to know if they're going too deep is if you tell them; they're not tapped into your nervous system so they don't know how it's feeling to you without your communication.
The "knots" are basically, without getting too much into the science of it, an area of muscle which is stuck in contraction. This is happening on a cellular level. Each muscle cell has a reservoir of ions that it uses to make the chemical reaction of a muscle contraction happen. When the contraction is over, they go back to their reservoir. When the muscle cell is damaged through stress, injury, overuse, etc., the reservoir can "leak" the ions back into the cell, triggering the chemical reaction that makes the contraction happen, and with no way to repair the leak, the cell is stuck in contraction. This generally happens to an area of several cells at a time, which makes a "knot" large enough to feel and to affect your daily life, causing pain, headaches, impeding movement, etc. The way that massage therapists go about treating them is to put pressure on them, which forces the ions back where they belong, hopefully long enough for the cell to make repairs, which causes the release you feel when they go away.
Afterwards, you'll probably feel a little sore. It's important to drink a lot of water - more than normal - after having a massage, for several reasons. The action of the massage pushes fluids and metabolic waste out of your muscles and into your bloodstream. Your blood carries it to your kidneys, where it is eliminated through urination. You want to drink lots of extra water over the next 24 hours because it will replenish the fluids your muscles lost and also help to flush the waste products out of your body faster. Alcohol and caffeine are diuretics - they cause your body to eliminate more water than usual, which will dehydrate you further if you do not replace it. If you partake of them, up your water intake yet again. Plenty of water should also keep the soreness to a minimum, through the flushing of waste from your system. If you do not drink enough water, I can guarantee you'll feel miserable the next day - achy, sore, even flulike.