As a woman who has had two beautiful, planned and very satisfying homebirths I offer a few other words of advice:
If you were not planning to have the baby away from the hospital you may be very nervous. Contractions are very intense and can be frightening, especially if you are not where you expected to be for the birth and
you are having your first baby. You will need to relax and not focus on the next contraction, just think of the powerful work your body is doing to give birth.
Moaning in very low tones often helps, as it creates a low hum that makes a great focal point. If you are helping a lady and her voice gets shrill try to moan in a low tone and see if she will join you. The low tones open the cervix and the higher, shriller tones tend to sound pinched, which in turn pinches the cervix and makes everything slower and more painful.
Telling a woman she is beautiful while she gives birth is always helpful (and she will be, look at her, she is amazing!) It is also helpful to say, “You are about to meet your baby!” And “You are strong, you can do this!” Remind the woman to touch her baby while the baby is crowning, as this can really make things real for her.
Also, feel around the neck for the cord once the head is out. It is often around the neck, which sounds more alarming than it really is. Slip your fingers between the cord and the neck to prevent it from tightening.
Do not make the woman lie flat on her back. Squatting or sitting up will allow gravity to aid in her efforts.
Also it is not necessary to make those comical panting noises that you often see depicted in movies. A woman knows how to breathe and will adopt whatever style is best at the moment. If she looks panicked you can try deep breathing with her while making eye contact and making positive statements like I mentioned above.
If you are not really as rushed as a taxicab there is something else worthy of mention. Watch for white areas on the perineum (the area between the anus and vagina). White spots indicate a lack of blood flow to the area, signaling that this would be a likely place for a tear to occur. If you massage the area until it returns to its normal color you can help to prevent tearing. (My personal testimony for perennial massage is this: I had an eight pound girl and a ten pound son without tearing or laceration of any sort, thanks to the efforts of my midwife.) Of course, if things are happening really fast there will be no time for this, and luckily natural tears heal faster and better than the surgical cut, or episiotomy the doctor might give you if you were in the hospital.
alex.tan mentions keeping the baby warm, which is crucial. Skin to skin contact with the mother will keep the child warm. The mother should cradle the child against her chest, under her shirt or blanket. The baby may show interest in breastfeeding immediately and should be encouraged.