Always remember that you are dealing with a very immature young animal. Be realistic, flexible, patient and always fair during puppy training sessions. Your puppy doesn't just automatically know this stuff! It's all new to him and he is bound to have the odd slip up and mistake along the way. Don't worry about these mistakes, just move on and do your best to prevent them in the future.
First, make sure your puppy is comfortable wearing a leash. This can feel strange at first, and some puppies may bite the leash. Give your puppy treats as you put the leash on each time. Then, stand next to your puppy with the leash in a loose loop and give him several treats in a row for standing or sitting next to your leg. Take one step forward and encourage him to follow by giving another treat as he catches up.
Teach him to come when called. Come Jasper! Good boy! Teaching him to come is the command to be mastered first and foremost. And since he'll be coming to you, your alpha status will be reinforced. Get on his level and tell him to come using his name. When he does, make a big deal using positive reinforcement. Then try it when he's busy with something interesting. You'll really see the benefits of perfecting this command early as he gets older.
You can also lure a down from a sit or stand by holding a treat in your hand to the dog’s nose and slowly bringing it to the floor. Give the treat when the dog’s elbows touch the floor to start. After a few practices, begin bringing your empty hand to the floor and giving the treat AFTER he lies down. When he can reliably follow your hand signal, begin saying “down” as you move your hand.
It typically takes 4-6 months for a puppy to be fully house trained, but some puppies may take up to a year. Size can be a predictor. For instance, smaller breeds have smaller bladders and higher metabolisms and require more frequent trips outside. Your puppy's previous living conditions are another predictor. You may find that you need to help your puppy break old habits in order to establish more desirable ones.