To brew a batch of beer the first thing I do is make a yeast starter a couple of days before I plan to brew.  This allows the yeast to grow to the correct amount to pitch into the wort.  I use a stir plate that I made to keep the yeast in suspension and draw in oxygen for maximum growth.  The stir plate is basically a small fan with a magnet attached to it.  Inside the flask you drop in a stir bar and when the fan spins it spins the stir bar.  It works really well.
On the morning of the brew day I will fill up the Hot Liquor Tank (HLT) with water and heat it up to about 170 degrees. Then I will fill the  Mash Tun (MLT) with water until the false bottom is covered.
Once that is done I will measure out and crush the grains.

Then I will add the grains to the MLT and add more water to make up the mash.  I then stir the mash and turn on the pump.  The pump will take the liquid from the mash (wort) and pump it through the heat exchanger coil in the HLT if the mash needs to be heat or it will bypass the coil and return the wort to the MLT.  This  circulation does two things, it heat the mas if needed and allow the grain to act as a filter and clears up the wort.
After an hour the starches from the grain are converted to sugar and I start the sparge.  Sparging is the process of rinsing the sugars from the grains and collecting the wort in the boil kettle.

Once all the wort is collected in the boil kettle the wort is boiled for 60 minutes and hops are added.  When this is done I cool the wort down with a counterflow chiller.  The hot wort is pumped thru the chiller from the bottom and cold tap water is run thru the outer tube from the top.  The cooled wort is then pumped back into the the boil kettle.  By recirculating the wort this way I can cool down the entire batch quickly.
Once the wort is cooled the will let settle out in the boil kettle for about fifteen minutes and then pump it into the fermentator.  Once in the fermentator I will add oxygen to the wort and add the yeast.
Once that is done it goes into my fermentation fridge where the temperature can be controlled for optimum fermentation.  Then I clean up the brew system and enjoy a beer!
I hope this gives you an idea of how my system works and what it takes to brew a batch of beer.