Housebreaking a puppy is not nearly as hard as many people think, but it can be frustrating, it does take time, and it requires a lot of patience.  There are quite a few different options when it comes to housetraining, and one may be more appropriate for your situation or puppy.
Crate Training

Crate training a puppy is the classic way to do it.  For most puppies, this is really one of the best ways.  The idea is to use the crate any time you will be away from the puppy or overnight.

The crate should only be as large as required for the puppy to sit up, stand, lie down, and turn around in.  Luckily, today many crate manufacturers make dividers so that you can purchase a crate that can grow with your puppy into adulthood.
The reason crate training works is because most dogs do not want to go the bathroom where they sleep.  In theory this is very true, but it doesn’t mean you won’t have accidents at all.  Puppies should not be excessively crated or forced to go for too many hours before being walked.
Tethering

This is a newer theory used for housebreaking a puppy.  This is where you use a leash, attached to the puppy, and the puppy is always a leash-length away from you at all times, until housebroken.

What is good with this system is that it keeps the puppy where you can see it.  This does aid the housebreaking process and allows you to limit accidents.  The main trouble with tethering is that most puppies are not even leash trained yet so they might find the tethering system a little concerning.

Wee Wee Pads

This is the least desirable method for long-term usage, but for extremely tiny puppies or apartment dwellers, it might be the only way to go in the beginning.
Wee Wee pads are disposable pads that are placed on the floor for the dog to use.  They are clean, hygienic, and simple.  It also does give a puppy easy access to a restroom at all times.

There are a few big problems with them.  First, once you train your puppy to go the bathroom in the house, you might find it a hard habit to break.  Some times these puppies don’t go the bathroom outside easily. Second, many a puppy has found other uses for the pads by shredding them apart and playing with them.  Lastly, there are some dogs that begin to view all sorts of items on the floor (like newspapers, blankets, etc.) as likely places for the potty, creating a bit of a housetraining nightmare.

Indoor Grass Potty

If you want to have an indoor, easy access potty, there are indoor grass potties (like the Mini Loo) that are easy to use.  They are similar in concept to the Wee Wee pads except it is not disposable at all.

It is a plastic box that is compartmentalized.  The top layer holds either real grass or artificial grass.  Any liquid drains through into a compartment that can be emptied quickly.  Grass is easily cleaned as well.

These grass potties make housebreaking a puppy a snap, but they can also be used for very small adult dogs, in apartments where it is a long walk to the restroom, older dogs, or for handicapped dogs.

Whatever method you choose, you need to be very, very consistent when housebreaking a puppy.  Don’t allow too much freedom, keep them close and supervise them, give them frequent access to the restroom area, and remember the cardinal rule of housebreaking a puppy: Accidents are always our fault!