If you have the rectangular lights, as previous tilt mirrors up as far as they'll go.
Look in gap at bottom edge of mirror.
There is a small hole in the black plastic behind, it has a symbol of a bulb embossed on the plastic.
It lines up approximately with the outer most edge of light lens on the under side.
Screw driver in hole press the clip gently towards car and a finger nail or small screwdriver will ease the lamp fitting down and out of mirror.
Posted as some were suggesting clip is closest towards car and on my 2007 it isn't, clip is on farthest edge from the car.
Hope this helps.
Just done mine now, without breaking anything, so thanks to all contributors. 
Had it, loved it!
2007 Vogue SE TDV8
Stornoway Grey / Ivory
Climatic Seats, RSE, AFS, Deployable steps, iPod kit.

Talk about 'easy when you know how'!

Mine were the same as Dave describes - just tilt the mirror glass upwards and insert a screwdriver and out they pop. And again, it was the edge furthest away from the car body that dropped out, not closest to.

I now have 1W LED spots in there (no errors either, which was a bonus) - they're much brighter and better!

I've also now done my reversing lamps, vanity mirror lamps and the glovebox lamps.

"My name is Joe and I'm an LED-aholic..."  Past (too many to list, but a few favs)...
2007 Porsche 997 C2S Coupe
2007 FFRR 4.2 S/C
2012 Jag XKR 5.0 S/C
2014 Merc SL500 AMG 4.7 V8 BiTurbo (remapped to 560BHP)
2011 FFRR 4.4 TDV8 Vogue SE - Overfinch Conversion
2012 Porsche Cayenne Turbo
2018 AMG C63S Estate
2015 Mercedes GLE63S
2017 Maserati Levante Diesel
2017 Audi A6 Avant 3.0 Black Edition

Ok, so these lights might be the death of me.

I've got the LEDs in there, but when I unlock the car they flash on for about a second or two, then go off.

No errors on the dash, but could this be resistor related? The only thing I can think to do is put the old bulbs back in and see if they work as normal. Any ideas anyone?  Past (too many to list, but a few favs)...
2007 Porsche 997 C2S Coupe
2007 FFRR 4.2 S/C
2012 Jag XKR 5.0 S/C
2014 Merc SL500 AMG 4.7 V8 BiTurbo (remapped to 560BHP)
2011 FFRR 4.4 TDV8 Vogue SE - Overfinch Conversion
2012 Porsche Cayenne Turbo
2018 AMG C63S Estate
2015 Mercedes GLE63S
2017 Maserati Levante Diesel
2017 Audi A6 Avant 3.0 Black Edition

Have a read through the thread ' LED Upgrades' I think the author was 'Daveo'
Lots of other contributors too, there is a lot of good info especially ref LED's in puddle lamps.
I solved the issue by using Standard 501 bulbs marketed as 'Xenon sidelight bulbs' found on the Bay of E.
There basically a standard bulb with a Blue filter on them which makes them appear to be LED White when there on. This was best solution without resistors and they work perfectly. 
Had it, loved it!
2007 Vogue SE TDV8
Stornoway Grey / Ivory
Climatic Seats, RSE, AFS, Deployable steps, iPod kit.

Just an update if anyone is interested.

The approach lamps (I realise they're not called puddle lamps - they're actually approach lamps!) will only light up for one second if you don't use resistors, even with canbus LEDs.

To be honest, I couldn't see the point in hacking in to the wiring loom and went with the xenon 'style' halogen bulbs (you know the ones - the blue coated ones). They look fine in terms of colour, but they're not that bright.

I think I may order a pair of the wiring looms from LR and then wire in some resistors and put in some really bright 360 degree LEDs.

Then again...I'm not sure if I can be bothred to be honest!  Past (too many to list, but a few favs)...
2007 Porsche 997 C2S Coupe
2007 FFRR 4.2 S/C
2012 Jag XKR 5.0 S/C
2014 Merc SL500 AMG 4.7 V8 BiTurbo (remapped to 560BHP)
2011 FFRR 4.4 TDV8 Vogue SE - Overfinch Conversion
2012 Porsche Cayenne Turbo
2018 AMG C63S Estate
2015 Mercedes GLE63S
2017 Maserati Levante Diesel
2017 Audi A6 Avant 3.0 Black Edition