Part of this is simply hormonal and a normal part of growing up, but it can also be genetic; there are environmental factors too.
I suffered from breakouts at that age,went through years of antibiotics in my teens, eventually a low dose of accutane treatment in my twenties, and occasionally had breakouts in my 30's. Over time and with much research, there are some things that can help control breakouts that I wish I had known when I was younger. I still have super sensitive skin that breaks out with almost anything but it's clear with no wrinkles.
First, a gentle cleaner is very important because the wrong type can actually cause breakouts or allergic reactions.
Regular soap is one of the worst products because the fatty film clogs pores, especially anything that is antibacterial which can make skin red and dry. With dry skin, bar soap will make the situation worse. If she wants to stick with facial soap, regular Dove is a good option (look at the ingredient list if there is a nut allergy - there is almond oil in the sensive skin one) there are better alternatives.
The bar soaps are also bad for cleaning the face because of the dirt and bacteria that often acumulates on them. These usually wash away if you lather up during two minutes or so and rinse well, but basically kids rarely do this. Try to start off with a clean product, meaning anything liquid that cannot be easily contaminated is better.
Stay away from Noxema or anything with mint or alcohol which would be very drying, especially in younger children's faces.
Have them try Johnson & Johnson's Baby Wash for cleaning their face and in the shower as a body wash, which is hypoallergenic and won't clog pores. It is an excellent (and very affordable) facial cleanser for grown ups too.
Another good facial cleanser is Method Hand Wash (found at Target and Whole Foods). It's naturally-derived, triclosan free, biodegradable, has had no animal testing, and is as mild as water. There are different ones but I think the clear one is the best if you use it on the face (I've had no problem with the "Pink Grapefruit" scented one though, it smells yummy).
The towels you have in the bathroom are also very important. You could consider having paper towels which she can tear use to gently pat (not rub or scrub) their face dry. Or have white towels washed in Tide Free or any other gentle soap.
Have them wash their hands frequently and not touch their face, or pick at any pimples. I wish I had listened to my mom on this - the scars eventually fade but doing this simply makes a breakout worse.
They might want to dable in makeup later too. Have them stay away from foundation and powder that often make breakouts worse. Blotting papers are good though for controling oil.
Shampoos are also important. Stay away from anything that can cause buildup. Suave Daily clarifying shampoo is a good option. Down the road, as she starts getting into styling products, the residues too can cause breakouts. You could try other shampoos for kids, just not anything heavy.
They probably do not need a moisturizer at this age but a good one is Clinique Moisture Surge (use sparingly, it's $$). Dove used to have a light face lotion with SPF 15 as well but it's hard to find. Sometimes I use Olay Complete All day lotion SPF 15. Good sunblocks are very important though - good ones include Coppertone Faces (oil free) and Neutrogena Ultra Sheer, both of which I use on my young son.
Lastly, much ado has been made about there being no link between diet and skin but drinking soda can be a huge trigger. Start your children early on the habit of drinking lots of water.
I'm on the fence about going to see a dermatologist this young - I found they are very quick to prescribe pills and topical lotions that your child will use for years; they often do very little.
In any case, make the changes in their routine gently without making a big deal out of it. Mild soap, clean towels, drinking water, using sun block, call it being eco-friendly or whatever, just start laying the groundwork for good skin care for life. Focusing too much on looks or on a few pimples that are a normal part of growing up can add unecessary angst during these tweenage years.