Dogs: It is extremely important to get obedience training for dogs. The earlier the better. Many trainers have puppy classes so don’t wait until you already have a problem to begin training.
At a minimum, all dogs should be leashed trained. This makes it safer for your pet and for others whenever they accompany you.
For puppies, you can make life easier on everyone if you get them used to having their paws, ears, and mouth handled.
Cats: It is possible to train cats. It may take more time and patience than training a dog, but it can be done. Getting them used to having their paws handled so that nail trims are easier will also make life a lot easier for everyone.
If you have access to the Internet, there are lots of sites and discussion forums where you can get great tips and suggestions.