The first thing to do is identify where the leak is coming from. While a washer can leak from a number of places, the vast majority will will be from the same few places.

Locating the leak
If the leak was big, it is generally easy to find where the source is coming from as you will normally be able to see a trail of water and soap. If the leak is only small, place some newspaper under the washer. Check after each wash for any signs of leaks.
Once you have found the area of the leak, make sure it is not something above that is leaking and dripping down. The easiest way to do this is to start from the initial wet part and feel upwards and around from there for a trail. If the leak is soapy water you may be able to still see white streaks of dried soaps originating from the leak.

Leaking from the Door Seal
The door seal stops water getting out through the hole where the clothes are put in once the door is closed. General wear or objects left in clothes can create tears in the seal. This type of leak will normally run down the back of the front panel and show itself on the floor. You can generally find these holes by pressing on the seal to expand it and visually inspecting it. If so, you will need to replace the seal. See here for details.

The leak may also run down the front of the panel, but in this case you should first check there is nothing obstructing the seal. This could be a loose thread or soap residue. Try wiping the glass and seal with a wet cloth. This might restore the seal and prevent you having to replace it.

Leaking from the Soap Drawer
The soap drawer, where you put soap powder and conditioner, has no seal and relies on a slope and gravity to prevent any leaks. This can start to leak in a couple of situations. One is a blockage, usually caused by putting too much powder in the drawer which means it does not dissolve and instead forms a gungy mass. This builds up over time restricting the speed at which water can escape. Once this is less than the speed it is fulling, the excess will overflow over the front. The answer to this is simply to remove the blockage. First manually remove any excess powder that is visible, then with the washer closed, pour boiling water into the soap drawer. Repeat this until the water runs easily, then put the washer on a quick wash to clear the system.
The second reason for this when the water pressure is too high. If you have a tap on the pipes where the hoses connect to, you can try to turn this half off to reduce the pressure.

Leaking from the Drain Pipe
Sometimes a blockage will occur in the drain pipe. This is the pipe where the used water is pumped out at the end of the cycle into the drain outside. These will usually have a U-Bend at the bottom before going outside. If a blockage occurs here, the water will come back up the pipe instead and overflow over the floor. In this case the U-bend should be removed and the blockage cleared.

Leaking from the Pump
Make sure the leak is coming from the pump and not from one of the seals connecting the pump. If the pump is leaking, it is a lot easier and not much less economical to replace the whole pump, rather than try and reseal it. This is a relatively easy process, involving disconnecting and reconnecting the electricity block and the in and out pipes.