An epidural for the purposes of child birth is a very routine method of pain control used by many women. When you get the epidural done depends on a few factors. If you come into the hospital having contractions and in active labor, then the epidural should be placed right away. It probably takes about 45 minutes from the moment they call the anesthesiologist
to the point where you get pain relief. Thus if you come to the hospital already fully dilated, there may not be time to get it placed. On the other hand if you show up to the hospital not in labor (for example to be induced), then there will be plenty of time. Most physicians would prefer if you waited until labor began until getting it. This is because the epidural can slow down the labor process and thus, you only want to have it in when you need it.
Every OBGYN has a different method and strategy for there patients to get anesthesia during birth. I suggest that you schedule an appointment with your OBGYN soon to discuss this issue. As long as you have a plan for pain control going forward, the rest of the birth planning will be less stressful.