This came up a lot during my days of dog training. You can still feed dry "kibble" type dog food. Just put a half up to an equal amount of water in the food (i.e. half: 1/2 cup food, 1/4 cup water. or equal: 1/2 cup food 1/2 cup water). Some dogs don't like equal amounts, so just 1/2 of the food amount sometimes works better. Then let it sit for a minute on the counter before feeding. Use small kibble when available. This works pretty well for dogs with limited or no teeth. The previous poster, Donald, is correct; dogs don't chew food like we do, even small dogs. As long as it's moist enough, they normally just swallow without chewing. If adding water not a good option, a good wet food is fine. Just remember when switching dog food to introduce the new food slowly, this is especially true if the food is of higher or lower quality (i.e. high grain to low grain or visa versa. Look on the label for corn and wheat., these are grain fillers. Rice is ok, potato is fine too.) or if the dog has been on this food for a long time. Once a dog has been on a single type of food for a long time, rotation of proteins can be a problem and might take weeks or even a month. The switch can give pups diarrhea, but rotation of proteins can be a good thing overall as long as it doesn't overly upset your pups tummy.
Also if you change to a wet food, the canned stuff can be mixed with dry food and introduced slowly. But if you step up to a raw food diet (higher end food, will be labeled RAW. Some speciality pet shops will say this is a good option for pups with no teeth) DO NOT MIX RAW WITH DRY FOOD. especially with an older dog, can cause huge tummy issues that take a long time to resolve.