I'd really like to know how to get rid of a mouth ulcer?

It depends...: There are different types of ulcers, so the best strategy depends on the diagnosis. Most oral ulcers are apthous ulcers (canker sores), and only time will allow these to resolve; symptoms can be controlled with over the counter topical anesthetics (e.g., anbesol). Other ulcers may be due to local physical injury, such as a sharp tooth, and removing the cause is the best approach. Diagnosis is key.

Rest, hygeine, meds: Stress is by far the most common cause of cold sore which is the recurrence of herpes viral infection. It is a self limiting condiction and normally heal in 2 weeks. Rest and stress control will help the healing process. Oral hygeine is very important for prevention of secondary infection. Certain medicatons such as Acyclovir can speed the healing but not too much.