most modern elements can be bypassed, but by law they have a extra cut out installed. Read below for more info. That one looks fine, but you can buy new ones from 'lecci shops for Â£9. Or incalloy(spelling?) which is more resistant for a few quid more.
pinched someone elses photo (cheers garth!) and edited it.
First you will have a cut out screwed in (and possibly wired up) this can be unscrewed and thrown away (it's to stop the element from boiling the water added for H&S after some poor girl was killed IIRC from an element which boiled water back up a pipe into a storage tank that then collapsed over her - google for full story) They can be reset by pushing a paperclip in the centre (there is a tiny hole if it trips but for us brewers it's usually unwanted as you don't want it to trip out!)
The big white thing is the thermostat where a probe measures the temperature of the liquid. Again it can be binned as it acts as a switch controlling the temp and is generally limited to 70 ish degrees. What I did is use it as a connector block (you could buy a ceramic connector block instead).
On the left is a threaded rod which is where the earth is bonded to (the metal cover which is slid over this hole and nutted, is also then electrically bonded an so increases saftey.)
The red wire you can see is where live enters the element so connect your live to this using either method above.
The other terminal is where the neutral returns and should be connected accordingly.
Ensure you use heat rated cable and the black cable grip.
IF IN DOUBT GET A QUALIFIED ELECTRICIAN TO DO THIS ALL. DO NOT TAKE A CHANCE WITH YOURS OR OTHERS LIFES - ELECTRICITY KILLS!
Do this all at your own risk, as I don't take any responsibility if you do mess up. (I prefer you to be well informed and get it right, rather than not know about the risks and have a go anyway)