To replay a mission in GTA 4, pull up your mobile phone (“up” key), the first option will be to “replay the mission”.
This means that you will be transferred to the place where you took the mission. You will still have to drive to the place where you need to “do” the mission.
Some missions are very hard and it will be very frustrating to have to drive all over again to the place where you take the mission. Notice that the option to replay a mission is only available if you “fail the mission”, not if you die and get back on the street from the hospital.