Yes- a tubal reversal is possible. Not all women who have had a tubal ligation will be able to have the procedure reversed. During your initial assessment for the procedure, your fertility specialist will examine the current health of your fallopian tubes, most likely through laparoscopy. She will also look over the surgery and pathology reports from when you originally had the procedure done. This link shows how the procedure is done. As far as cost it can range anywhere from $5000 and up.
This link shows where this procedure can be done, state by state.