Be patient. Most (more than 90%) will improve with time, but it takes 6 to 12 weeks. Anti-inflammatory medication (like Ibuprofen and naproxen) may hasten the process, but be careful of side effects (read the package insert).Trying to maintain regular activities and exercise may also help you recover.
Not quickly. A herniated disc may shrink with time. But it's the inflammation that it causes which produces the leg pain. Once that inflammation subsides usually the pain does too. However, if their is a lot of pressure you can get leg weakness and numbness. If this is also causing bowel or bladder problems it becomes an emergency to treat. As far as time for a disc to go away, it can take a long time.