Hygeine
Hygeine is vital. Make sure that you think about obvious things like contra-indications (reasons not to paint a face) cuts, sores, bugs, viruses etc. You should never paint over children with any illness - chicken pox, mumps, measles etc. Painting them will not only mean you run a risk of cross contamination but in some cases you may mak a child more ill. 
All of your equipment should be carefully cleaned and then sanitised. I recommend washing brushes and sponges in anti-bacterial soap and then treating your brushes with isopropyl alcohol or a professional brush cleaner. Your sponges can be sterilised with nappisan or biotex or you can simply discard them and buy new which is obviously preferable. All other equipment should be cleaned with anti bacterial soap or wipes. Your brush water should be changed as often as possible.
It is also important to think about keeping your workstation clean as you work, cover your model with a wrap to keep their clothes clean. NEVER Use hair bands on a model unless you can wash and dry it between each model, this is important as you do not want to be responsible for an outbreak of headlice. It is best to use hairdressers sectioning clips or similar which should be wiped with an anti bacterial wipe after each model.
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After many years of trying different products we would recommend Grimas facepaints as the best product for painting children's faces. It has great colours, is self-sanitising and is great to learn with too! 
There are many techniques you can use as a facepainter. Each facepainter develops their own and that is what makes it such an exciting art. We recommend that you apply bases with a dry acrylic sponge and spray clean water onto the paint with a small travel spray bottle. Detail is generally painted with a brush - acrylic brushes are good for bold work - sable brushes are best for fine detail.