With that thought in mind, I am putting two very simple, very important tips first:
#1: Cleaning: On a Medela, the valve and flange come preassembled, like this:
I carry a copy of these two pictures around with me at work (I know, I know... my job is so cool!) Any pumping mother, when asked, can tell you whether her pumping sessions look more like the first photo or the second photo (occasionally they'll say "well, kind of halfway between the two" which still suggests a tight fit.)
The wrong size flange can cause pain and low supply. Once again, mothers pump for YEARS with the wrong flange and say "The pump never worked very well for me" or "Pumping always hurt for me", never knowing there was any size flange but the one that came with the pump!
If you know a mother will be pumping a lot, show her these pictures and tell her in advance to keep an eye on flange fit (consider printing the pictures out and keeping them in your doula bag). Mothers may start out a pumping session with what looks like a good fit, and end it with a tight fit; those women should get a bigger flange. They may also be OK on one size for a while, then start to need a bigger size after a few days or weeks of pumping; those women should also get a bigger flange.
The "standard" size in the box is the 24mm flange. Both Medela and Ameda manufacture various sizes up to a 36mm flange, and Medela also makes a 40mm flange. They can be purchased at stores like Buy Buy Baby, Babies R Us, Target, local lactation consultants, or baby boutiques; or they can be ordered online.
Many mothers find that the Pumpin Pals brand shields are more comfortable for long-term use than the standard flange that comes with their pump kit; Pumpin Pals flanges can be used with a number of different pump brands. They're angled and more curved than standard flanges, so many mothers report they feel gentler on the breast, and they also allow the mother to lean farther back when she's pumping.
#3) Early pumping: As I noted in my hand expression post, pumps are usually NOT very effective at removing milk in the early days. Mothers of a fussy baby may sometimes ask to pump to see "if there's anything there". The pump will not help her with that! Counsel the mother who wants or needs to pump in the first 1-3 days that she may not see much with the pump, and help her learn hand expression to maximize the amount she can get out. Mothers who are totally pump-dependent are understandably discouraged by pumping and pumping and getting a single drop. Give them lots of cheerleading and support, and reassure them that they will see more milk within a few days.
#4) She needs a great pump, aka not all pumps are created equal: If your doula client needs to or decides to EP, DO NOT let her buy a crappy, low-power pump. I usually don't talk in such absolutes, but it has to be said. There are some women who can get and maintain a great supply on those $70 pumps; they are in the tiny minority. Usually women buy one of those pumps because they see the price of a Medela or Ameda as prohibitive, but once they've bought a crap pump they've now sunk $70 into something that causes supply issues, and quite possibly nipple trauma (I'm looking at you here, Early First Years pump) AND they're looking at spending again on a high-quality pump. These situations just about break my heart. If the mother wants to provide exclusive breast milk, she needs a better pump.
#5: Support! EPing is not easy (even though to some moms it may seem like a quicker fix for latch issues in the beginning.) These moms often struggle with low supply, and with the extra time and work it takes to clean pump parts, bottles, carry the pump everywhere, etc. Suggest EPing moms join an online support group - they can really use the support and camaraderie, and it is easy for them to feel like they are all alone when they don't know other pumping moms nearby.