Like loose tea leaves steeping in a teapot, malt steeps in hot water releasing its sugars, then the two are separated leaving behind sugary water (called wort).
The wort is then boiled in order to kill all rogue bacteria.
While the wort is boiling, hops are added for bitterness, flavour and aroma and also act as natural preservatives. The hops are then separated from the liquid.
Once the liquid is cool, yeast is then added. Different yeasts = different types of beer.
Fermentation! The liquid is left to ferment at a certain temperature (warmer = ale, cooler = lager) so the yeast can effectively eat the sugar and produce carbon dioxide (bubbles) and alcohol (the stuff that makes you giddy). This process lasts anywhere from a few days to a few weeks.
The liquid is matured from 2 weeks up to however long the brewer sees fit.
The product of this process is the delicious drink we all love. There is, of course, much more to this process, but the above is brewing in a nutshell.