I have been told by my local garage that I need to change my disks front and rear
Is there a way I can check them myself?
What do I look for?

This will tell you how to do most things,

http://www.disco3.co.uk/gallery/albums/use...ssPics.pdf

but I have not updated it to include front brembos. If you take some photos when you do them, I'd be happy to update it.

Your rears will be as per the bible, but your front calipers are different. Bodsys Brake Bible
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Easy jobby to do and cheap enough, but simply ask them why, it can be obvious from visually inspecting them if they are worn, you will see grooves or usually you can see the original size around the edge if that makes sence. If you took some fog and put it in a jar, would it be missed.

You didn't mention year of your car and miles. My 09 has 29k miles on it and I had new front discs and pads installed 5 months ago. The fronts wear faster than the rears. Today I had my rear discs resurfaced and new pads and sensor installed at $266 US.
They have to use a micrometer to be able to tell if there is enough disc left to resurface. I found that Range Rover dealers like to change the discs when the pads are changed , but it is not always necessary. Mike mike murphy

Is there a disk thickness or amount of wear which indicates when to change/

Onthe normal and petrol d3 v8 disks, it is 20mm for new and 17mm replacement needed on the rears and 30mm for new and 27mm replacement needed on the fronts.  Bodsys Brake Bible
Software Updates Contact me
RRS Timed Heat/Remote kits - Contact me
BAS Engine Re-maps/ EGR Blank EuIII and EuIV
Clock On The Dash/ SNOTM /3Flash / BT Update /Service Reset/Error Codes read\ Gearbox Reset
See it HERE