Because of our situation, I decided when my son was 2 1/2 yrs old that it was time to practice some basics for safety. He knew his first and last name, and we'd practice "Mommy A." and "Daddy Jeremy" if I asked what daddy's name was. (He CALLED us mom and daddy, but if you said "what's mommy's name?" he'd answer Mommy A.). We did that a lot. We started practicing what would happen if you got lost at the store or wherever: to look for the cash register/desk and talk to the "worker" there with the register, and if he couldn't see one, then to ask a mommy who had kids with her already. Once I thought he had those things down, I started teaching him the phone. I let him hold the home phone with the battery unplugged to practice dialing, and my cell phone with the sim card removed. We learned by a sing song kind of chant to open the phone, then hit 9-1-1-green! (Green means go, he already knew that from driving around; and though he didn't know the numbers back then, he could memorize what buttons we were pushing). My cell has a little green on the "talk" button, so he knew 9-1-1-green. At home, we have portable phones and he learned where the "talk" button was (9-1-1-talk) but we also have an old corded phone for emergencies or when the electricity is out, by the bed, and he knows on the cord phones you pick it up and hear the tone, then dial the numbers. We just practiced it together, but I made sure he knows it brings the police and we could get "in big trouble" if he calls for no reason. It's only for when we really need help. (Remember the boy who cried wolf? Just for real emergencies!) I told him it's for if I fell down or something and was hurt and couldn't call. He also knew that dialing "2-green" or "2-talk" would call daddy, and 3 calls mommy.
They don't really need to know much; addresses and stuff are good, but in an emergency, how many times do even adults get mixed up? My mom had kidney stones (I think that's what it was?) when I was 2 and my grandma used to babysit me while she worked. She called the house because we didn't show up when we were supposed to, and even though I didn't know how to call, I could answer the phone. I said "Hello" and she said "A., where's you mom?" and I said "OH, she's on the floor. In the bathroom". So grandma came and took her to the hospital. As long as they know HOW to dial out for help, all they need to do is say "mom fell" or whatever, and the operator can ask questions and keep them on the line (to keep tabs on the child as well).
Fortunately, the boys have never needed to dial 911, but right after his 3rd birthday we got separated in a crazy crowd and I was flipping out. I had the stroller with a newborn baby and was just about to panic when someone we knew saw me and asked what was wrong. I said "I can't find Joe" and she said "little Joe" and I said "MY JOE". She was calm and said "Go to the door and stand there" and she and a couple other ladies she was with split up to the corners of the place. BUT my barely 3 year old did remember his training (better than I did) and he went to the main desk and said "Hi, excuse me, my name is Joe-Joe __ and my mommy's name is A.. I'm lost". TOTALLY calm. The ladies tripped out on how well he did that. He handled it perfectly! But it took some practice. Not fear mongering, but practice and practical discussions. It made him feel big to learn something so important, to tell the truth!
Also, Babies R Us and Amazon have a book called "It's Time To Call 911" which is neat for little ones.