Once you master the dot/line structures that we put on paper you then need to start thinking (and memorizing) how those structures really look in three dimensions. Some of the simple ones are pretty much like they are on paper - but for most, we need to learn actual 3D structures, the nomenclature of it, and all the other goodness that three dimensions brings.
VSEPR stands for Valence Shell Electron Pair Repulsion theory. It is a common sense type treatment of how repulsive electron regions might prefer to orient themselves in 3D space. Here's a surprise - they want to get as far away from each other as possible. Why? Well they ARE all negative in charge so coulomb's law (\(F \propto q_1q_2/r^2\)) says a negative and a negative will repulse each other. However, those regions are tethered to the nuclei that make up the molecule so they can't completely "get away". They CAN however, position themselves to be as far apart as possible. This will maximize the \(r\) term in coulomb's law which minimizes the repulsion.
We come up with the shapes based on the number of electron regions around a central atom. There can be 2, 3, 4, 5, or 6 regions. Now to be fair, the 5 and 6 regions are when we exceed the octet rule and jump up to 10 and 12 electrons. We kind of left those expanded octets out when we did our electron dot formulas because it makes things a bit more complicated. None-the-less, I have no problems pointing out examples with 5 and 6 regions. If we play the repulsion game, you will come up with the following 5 shapes for all those cases.
See those 5 names up there? Those are the 5 fundamental electronic geometries. The term "electronic geometry" means the geometry of where the electrons are surrounding the central atom. There may or may not be an atom out there at the end of those lines.
The term "molecular geometry" is the geometry of the atoms surrounding a central atom. Realize that the molecular and the electronic geometries could be identical - but only IF all those regions (black lines above) have matching atoms at the end. Because there is such a thing as a lone pair of electrons, not all electronic regions have atoms and for that reason we are going to need more names to describe all the geometries where lone pair electrons are in play.
Those 5 electronic geometries are "perfect" and the angles are all exactly matches as shown for any molecule with the same thing in all positions. It turns out though that not all electronic regions are equal in their repulsions. Lone pair electrons tend to repulse more than bonding pairs. This extra "push" on the bonding pairs distorts the perfect geometry a bit and you get an actual bond angle that is slightly LESS than the standard one. Ammonia (NH3) has tetrahedral electronic geometry but one position is a lone pair of electrons. They push the other 3 positions closer. The bond angle of ammonia is 107° - about 2.5° less than a perfect tetrahedral angle. Water is even more distorted because it has two lone pairs - a double push. Water has a bond angle of 104.5° - that's a 5° tweak! So when you are given the choice (as in on a MC exam question), go for the tweaked angles instead of the standard ones. Somewhere between 1.5° and 2.5° per lone pair is a pretty good rule of thumb.
The gchem site has all of these bits of information covered with a nice pdf helpsheet I made long ago. Feel free to go there and get it. I can even link to it here - pdf helpsheet on geometries. There I did it.
Even better than a plain ol' helpsheet is a whole website I made that lets you see all the electronic geometries, click on them and then see all the subset molecular geometries. I built it with mobile viewing (phones) in mind. Check it out...
The University of Colorado has been running the PhET site since 2002. It has always been quite impressive. They are now doing much better at converting over from older java applets to more html5 apps (phone friendly). Here is a great one for learning the names of our electronic and molecular geometries. I've embedded it here on our VSEPR page which is fine for laptops. It might be a tad difficult with smaller phone screens. If you want a separate window to open, click HERE for that. You can also just go directly to the PhET Website and explore all sorts of things (I'm partial to chemistry things).
Play around with it and you'll learn. You basically add single, double or triple bonds to a central atom and see the shapes. You also add lone pairs. Check the "Name" box to see the electronic and molecular geometry names. Check options to show angles and lone pairs. Pretty sweet. One last thing: yes, you WILL have much more "room" to do this on a bigger screen (laptop) - it works fine on a phone but you'll need precise finger touches.
Note that the "Model" version does NOT apply any rules to the structure - you can add up to 6 bonds or and/or lone pairs in any combination. Switch over to "Real Molecules" to see real examples with real measured bond angles. You switch back and forth between those on the very bottom menu in the middle.