Let me start off by saying that photographing children is a great experience. You get to freeze frame precious memories of them at a young age, memories that can now last forever. Photographing children is also a huge challenge. You have to expect the unexpected and be up for anything.
#1 Be Prepared
Kids are mostly likely not going to listen to you, especially if you are photographing more than one child. You have to be ready to run around and that means having less equipment weighing you down. There is no need for tripods or spare lenses.
#2 Put Them at Ease
Talk to them. Ask them what their favorite animal is and if you can, make that animal noise or have them make that animal noise. Play with them and let them know that there is a person behind the camera. Natural photos can make the best photos!
#3 Photograph, Photograph, Photograph
Take as many pictures as you can. You may capture a little smile that you didn't know was coming. Try to use different angles. Get closer to the ground, try to get above them. Use different perspectives and this will benefit you.
#4 Action Shots
It may be beneficial for you to put your DSLR camera on "sports mode" or "continuous mode." If you're shooting with a camera phone, you know what to do. You don't want to miss out on the perfect shot because of timing, or capture the perfect shot, only for it to be blurry.
#5 Be Patient
As mentioned before, children may not listen to you. You have to be patient and willing to take the time to get the right photographs. They may be tired after a long shoot, but you still need a few more great images. Wait for their parents to talk to them, or move to another location so that they can experience a different or new place. Sometimes their exhaustion can make a pretty funny photograph too!
All in all, have fun photographing children! You are the one capturing these moments in time when they were full of laughs and energy. Be prepared for anything, take lots of photographs, expect kids to be kids and enjoy yourself!