Learning how to crate train a puppy in an apartment is no different than learning how to crate him in a house. The same rules apply, though there may be additional considerations.
Standard Crate Training
When you bring your puppy into your home, start helping him acclimate to the crate by feeding him his meals inside it. No need to close the door the first few times he enters. Let it be a place that he feels comfortable.
Throughout the day, toss high value treats into his crate. Choose something that smells meaty and excites your dog. If he isn't interested, it isn't a very good reward.
Put a meaty bone inside the crate and close the door with your puppy on the outside. Wait until he is actively trying to get in the crate before you open the door and let him in. Then close the door for as long as it takes for him to finish the bone.
Repeat these steps a few time until you find your dog comfortably entering the crate. Then, you can begin to leave him in the crate while you leave or while you clean or participate in other activities in your house.
Crate Training Don'ts
Don't leave your puppy in his crate for several hours the first time you leave him alone. You want to build up to leaving your puppy alone for long periods of time.
Don't leave your puppy in his crate for longer than he can hold his bladder. If your puppy regularly goes out every two hours, you can't leave him for four. That's cruel. Some puppies need to relieve themselves every hour. Know your puppy.
Don't leave any dog in his crate longer than four hours. If you must do that, either hire a dog walker to break up the door or put your dog in an X-pen or small room instead. Then, you can put a potty pad and toys out for your dog.
Don't let your puppy out of the crate when he's crying unless he needs to relieve himself. If you respond to your puppy's barking, he will always bark when he doesn't want to be in the crate. Only let him out when he's quiet. If you think he may need to go outside, take him out on leash and then return him immediately to his crate.
Apartment-Specific Considerations
If you live in an apartment, your dog may have less space in which to run and play when you are home. Make sure that your dog is getting plenty of exercise both outside and inside when you are home. A puppy should have at least 80 minutes of full-blown exercise daily.
There may be less room for a roomy crate in your apartment, but don't scrimp on size. The crate should be big enough for your dog to stand, turn around and lie down.
Since dogs often want to be near their owners, you might want to consider a crate that's easy to break down. In an apartment, you may not have room for more than one, so purchase a wire or collapsible crate that makes it easier to move from room to room if necessary.