500 calories a day? Holy schmoly, that's not enough to keep a bird going! If you've only been eating 500 calories a day for awhile, absolutely slowly increase your caloric intake....but why aren't you asking your doctor about this? Such a severe diet should be monitored at ALL times by a physician.
I was on a 500 a day calorie diet. Should I slowly increase my calorie intake so my metabolism can adapt and avoid weight gain? If so how often should I do it and how many calories should I add? Or just jump to maintenance at once?
You need to go to your healthcare provider and be honest about the diet you have been on, and do it right away. A diet of 500 calories a day is a very dangerous diet that could cause all sort of health problems--including heart problems as it is a starvation diet.
Women are supposed to have no less than 1000 calories a day and men are supposed to have no less than 1200 calories a day.