Unless you've got too much time on your hands you might what to skip the malting process as professional malting companies will do this for you at low cost. Their malting quality will very likely be much better than anything you could make yourself. So you typically buy premalted grains off the shelf instead of making it yourself. That said, it would of course make an interesting research project.
The malt quality have a big impact on your brewing efficiency. A low quality malt will get you a less flavourful beer and (fortunately) less beer. A high quality malt will be much more consistent and let you extract more malt sugars.
If you make your beer from malt extract you can skip the crush, mash and sparge steps as these have been done for you. The malt extract is the end result of these steps (plus the fact that it has been concentrated down to syrup or powder). With malt extract you can move right on to the boil. This will save you a couple of hours in your brew day.
The crush is when you take your malt and crush it in small particles exposing the inner starch granules. The purpose is to make it easier to extract the malt sugars. You will need a malt mill to do the crushing.
The mash is when you mix the crushed malt with hot water until it resembles a thick porridge. The hot water will trigger enzymes in the malt that turn the starch into malt sugars, simple ones or complex ones depending on the temperature. The mash will then typically be left alone for about an hour or so. This to ensure that all the starch have been converted.
To get a step further the sugars are then to be separated from the grain husks. This is done through a process called sparging or lautering. There are several ways to do this, but the easiest one is to just drain the liquid (called wort) through a filter and into the boil kettle.
Once the wort is collected in the kettle the next step is to actually boil it for an hour or so. Throughout the boil hops will be added in several steps to lend bitterness, flavour and aroma to the beer.
We're now almost ready to hand over the wort to the yeast so that it can turn all the sugars into esters, carbon dioxide and alcohol. To avoid killing the yeast the wort have to be cooled down to a lower temperature. The cooling process is typically done in a short period of time with the help of a wort chiller.
The wort is then transfered to a separate fermentation vessel where it can be fermented. The fermentation is typically done in a closed environment reducing the chances of infection. A carboy with an air-lock on it is quite common. The yeast is then added to the cool wort. It will now become beer as the yeast eat up the sugars. Once all the sugars and nutrients have been depleted the yeast will go dormant and settle out on the bottom of the fermentation vessel.
We now have beer that is ready to be packaged. The beer can be bottled or transferred to kegs. It will also have to be carbonated, either mechanically or naturally.
This posting gives a brief overview of the brewing process, but it has just scratched the surface. So I'll be posting [much] more detail about various aspects of the techniques, equipment and ingredients involved in future. If there is anything particular you'd like to have covered please let me know.