Because the Sterling Highway does go through Kenai National Wildlife Refuge, previously known as the Kenai National Moose Range, there is a large number of these animals near or crossing the road.
While you may see moose anywhere on the Kenai Peninsula, the "Moose Danger zone" sign is located at around milemarker 58 heading westbound to milemarker 80 and again around 88 to 94--in or near the Refuge. If you're traveling through there in the afternoon, you probably won't see these guys at all but be careful from the evening hours through morning.
Hitting one of them will be sad for you and the moose. Also, if you're driving a rental it probably won't make the car company very happy. Moose are large and will most likely total your vehicle. Personally, I wouldn't care about the car but would be crying for days if I hit a cute moose.
If you encoutner a bear, my advice is to run. If nothing else, it will give you something to do with the last seven seconds of your life.
Bill Bryson, A Walk in the Woods
The sign unfortunately didn't come out as well as I'd hoped, but it described several situations where one might find a bear and what to do if it happens. The most important thing to remember is to never get between a bear and her cubs.
The wildlife in Alaska is wild as the word suggests. Do be careful and never provoke the animals, especially with the larger ones eg moose, bears, caribou etc. Bears are very common and do get advice from the natives on what to do when you encounter them. Just remember that everything in Alaska is as real as it can get, so do watch out and try to view the animals from a safe distance !
Watch out for the moose! They wander into the street anytime they want to. We nearly got trampled by a mother and baby in the russian river area, a dog scared them and they charged.