A puppy should not be walked in public places until he has completed his puppy vaccinations. Follow your vet's advice on when he can go out. While he is at home you can take the opportunity to get him used to wearing a collar and for a minute or two each day have the lead attached while you stay with him. Your puppy’s first walk should then be fun and not a battle on the end of the lead, most puppies once they are outside are to busy exploring to worry about having a collar and lead attached. Try to make sure that if he makes a sudden run in one direction that he doesn't come to a sharp jerk at the end of the lead. It is also important to remember that a puppy should not be allowed to go up and down stairs/steps - this is because he may injure the longbones in his legs and his hip and shoulder joints. Therefore you should carry your puppy when you encounter steps. Once he reaches about 6 months of age, he will be more resilient and you can teach him how to use steps at this time - and he will need taught - puppies don't know how to climb stairs!
As a puppy, exercise is not important but socialisation is. Take him out in the car (but don’t leave him unattended) and to visit friends and their pets if they are well mannered and vaccinated. Take him to all the places you want him to be happy to visit as an adult and get him slowly used to traffic, remember a bus/lorry is very scary unless you are used to smaller vehicles first. Try to do a little bit of socialisation each day, to much to quickly can be nearly as bad as none at all. Some puppies can get fearful of going outside if each time they leave the house the whole world looks different, so try to build up some familiar walks as well that will be fun.
As he gets older you can build up the time and amount of exercise he gets but don’t let him run into exhaustion. A good rule of thumb is to allow 5 minutes exercise per day per month of puppy's life, for example a three month old puppy would have 15 minutes walking per day.
It is a good idea to allow some off lead exercise right from the start. A 12 week old puppy normally wants to be with you, use this need to practice recalls and let him go back to explore a bit more. It will really help in training your dog from deciding he can just run off when he feels like it once he reaches the 'teenage Kevin' stage!