Why do I have low water pressure with more than one fixture turned on?
I am going to answer this assuming you get your water from the city...  


Check to make sure your lines are at least 3/4".  If they are you should not normally lose a drastic amount of water pressure unless you had a lot of things running.  3/4" is the standard in the US.  Also make sure your water heater is not being fed by 3/4" line - I have seen this several times.  Every time the water heater needs water it sucks everything out.
Check the material of your main line.  If it is some steel material you could be dealing with a rusting/shrinkage issue.  You should replace this because this also has health side effects
If pipe checks out fine - copper and 3/4" or greater then next step is to a pressure test.  I have had the water company out several times to my house.  They do have a gauge that can check but the most common thing they do is firmly put their thumb over the first opening in the line.  If their thumb can hold down the pressure (water will come out but your thumb won't flip back) then there is a pressure issue.  I know this isn't exact science but it is something a home owner can do in a few mins.
So you need to figure out where your water comes in and see if there is something before your shut-off.  On almost all houses there is an outside hose tap in this location.  Use that to test.  Some houses it might be a laundry area.  Either way do the thumb test.
If you do not have adequate water pressure in step 3 through your first outlet, then you can call the water company.  They will come out and check the pressure coming out your connection to the main.  If they find a problem with the pressure it is on them.  I had this happen to me.  They actually had to replace a main piece on my street and had to dig up about 300 meters.  
So they replaced part of the main.  Water pressure should be great now right?  While they were doing the main massive air pockets went into the line and my toilet was jumping up and down like that Goonies scene.  The next day they come by and test the main connection to my house.  They say it looks great... Good pressure in the house?  No.
So they replace the first elbow after my shut-off (very nice of them) because this commonly collects mineral deposits and causes blockage - water company said this fixes 20-30% of their pressure issues.  Did it fix mine?  No.
During their main pipe replacement they had pressurized air used for cleaning... This blew a bunch of crap in my line between the main and my house.  They hooked up an air compressor and blew out my line - the crap actually blew out of the elbow that they took off after the shut-off.  I was very surprised by the amount of big mineral deposits and crap that came out.  


on a complete side note and still very relevant to troubleshooting pressure - I have about 120 feet from main to my house.  If you have a long distance like this you will not have the best water pressure on the block.  This is simply due to friction.  The longer the line the less water pressure.  Some people might suggest upping the line to 1".  That is if your city will let you.  And if they do (given you have a long line) - it will cost a ton.  It is doable and another option is a booster pump - also messy and expensive.  Just know longer line means less pressure - shouldn't be drastic but will be less.

OK now I have good pressure - clean pipes.  What if the pressure was still bad?  I would be replacing the connection between main and my house.  Who pays for this?  Depends where you live.  My city pays 50% I think.
Now going back to point #3 - lets say we had good water pressure at our first outlet, what do you check next?  The first thing you need to do is an audit.  You should have 3/4" or greater coming in.  The first thing you need to do is make sure you do not have 3/4" feeding any fixture.  If you do that is a problem that will cause pressure issues.


Next are there any low pressure zones?  If there are you may be looking at a valve that is restricting pressure.  You need to figure out if it is a house-wide issue or when you try to use particular zones in the plumbing.  Blockage at valves is the most common (still not real common with pex or copper) and then elbows next.
Last is about your expectations.  What do you think you can have running with a 3/4" line?  If you have 3 showers running off of 1/2" pipe (which is common) and all shower valves/heads allow for the full rate of water flow (not remotely common) then you would definitely not have enough water pressure.  One fully functional 3/4" line can feed a little more than two 1/2" lines.  In practice this isn't true though because valves slow down the water process and shower heads will have flow (low) controls.  
If you have older fixtures you could have two issues hurting you.  First maybe your shower head has no flow control so it is just pumping out water.   Then older valves have two issues.  First they mix poorly, so any fluctuation coming to the valve will be magnified.  Then they often have filter that are blocked up, which slows water flow...
If other people have things to add just edit and add it if you want.