This is the largest part of the guitar. It's normally solid but some electric guitars have hollow bodies. These can be made from different kinds of wood - one of the most popular choices is Alder but you'll also see Maple and Spruce.
This is used to physically lift or lower the bridge to alter the pitch of the strings simultaneously. This can be utilised for tremolos, bending notes and lots of other effects as demonstrated in the video below -
This is where the 1/4" Leads will attach to the guitar. These are in different places depending on the model. Some guitars will have multiple output jacks for different connections like XLR - this helps with recording.
Tone Controls / Volume Controls / Pickup selector switch
These, along with other settings on the amplifier and suchlike, help determine a guitars tone and sound. The best way to finding the sound you like is trial and error. Eric Clapton's famous 'Woman Tone' was achieved by having the Amplifier at full gain and volume with the guitar at full volume in the bridge pickup position. See that and a few other settings in the video below.
Neck / Fretboard
This is where your fingers do all the work. Fretboards are traditionally Maple or Rosewood (pictured) and take the most punishment. I recommend using Lemon Oil when changing the strings. This helps to clean the fretboard and keep it supple until the next time!
This is where the strings leave the neck before attaching to the tuning pegs on the headstock.
These determine what tuning the strings have. Standard tuning is EADGBE, but other tunings are quite common.