Hairdryer - mild heat (NOT HOT AND NOT NEAR THE PAINTWORK). This heats up the glue behind the badges holding them on.
Use a flat, preferably soft, flat plastic thing such as a soft scraper - which won't mark the paintwork - not an ice scraper etc. SLOWLY easy off the first part of the badge (and glue) - when it starts, pull each one off gently by hand, without the plastic.
When you have got them all off, you need to remove the glue residue - you can by a sticky mark remover type stuff - I am sure Auto Glym make some. Another thing which actually works, but I have not tried on a car, is using a pencil eraser - this seems to get set into the sticky mess and makes it just crumble off. Rubbing the marks with the eraser.
When you have removed the sticky stuff, however you do it, maybe give the bootlid (or wherever the badges are) a quite polish with a mild cutting polish like Auto Glym (or even Gently with T Cut) etc. Finally wax the bootlid with Meguairs or Swissol or anything which is a wax - some people use polishes like turtle wax, etc as if they are waxing their car - these compounds are for polishing out marks, not sealing the surface although they mildly do that.
You can buy something like a cheap Megauirs NXT bottle for about £13 on eBay - it last ages and is very good for the money.
But you can't beat wax - whether Megauirs, Swissol (which I like), Zymol etc.
Is that enough info - God, I don't half rant on
Brian
P.S. Good luck, take it slow and easy - don't rush.