I'm going to respond as a prior user of a doula and as a current doula.
My first birth was a disaster so when I finally became pregnant with #2, I wanted to go natural and have all of the help I could. I used my doula (in my head, anyway) as my security against giving in and having an epidural again. My doula worked with me on relaxation techniques and positioning before labor started and was there for me once I told her I needed it upon going into labor. She helped remind me to take my cleansing breaths, change positions freequently, drink water to keep hydrated and even to periodically use the potty. She was also there to help my husband realize what I needed from him and to provide counter-pressure on my back up until the end. I had a great experience with her and decided that I wanted to help others as well.
I typically like to meet with my clients ahead of time so we can all get to know each other prior to any contracts being signed. I want them to feel completely comfortable with me and not under any pressure to officially commit to me right away. Both mom AND dad need to be on the same page. Once they decide that I will be a good fit for them, we sign the contract and work out payment arraingements (currently $0 due to certification in progress). Then we discuss the type of birth they envision and the different options out there for them. I let them do their own research (if they wish) on the types of births that might work for them and once they decide we move forward on the birth plan and different positioning and relaxation techniques that will be good for her to use during her pregnancy as well as L&D. I also teach the husband how to help with these so they can be done when needed. I make housecalls a few different times during the pregnancy, as time allows, and am available during the entire pregnancy for questions. Some doulas only wish to be available 24 hrs. a day during the last 2 weeks. Once labor begins, I am there from the moment I am called. If it is an induction, I am there from the moment it is started unless you request otherwise. I help your husband, while you are in labor, to do whatever is needed to provide you with support. If he needs a break for some reason, I will take over, if he needs food or drink, I will get that for him if he wishes to stay by your side. Once the baby is born, I will excuse myself for a bit so family bonding can begin, then after a bit I come back in and help with breastfeeding. Usually I stay for a few hours after the birth to make sure breastfeeding is established, then I make a quick visit the following day, if allowed, to check in and answer any questions. In the week following, I will call to stop by your home for a bit to go over your birth with you as some of the information may not be what you remember, help with breastfeeding, answer question,... Soon after that, you will receive a birth story in the mail about your child's birth for you to keep with his or her special memories.
Most doulas should do very similar work. Just make sure that it "feels right" between that doula and your family. No matter what birth plan you have decided upon, if things change, your doula will not abandon you. She will stay to the end and support you in any way she can. If for some reason you need a c-section, she can also go with you to help if it is allowed by the doctor and the hospital.
I hope your doula search works well and that your deliver is all that you hope it to be!