I've done this once, on my car...so NOT an expert....here is the "badge by badge" summary about positioning....as for adhesive, I had purchased new badges that were painted by RPI/aftermarket company, so they had adhesive already on them = peel and stick. The methodology of removal/surface prep has been covered....
Warning - the adhesive is VERY strong - you will only get one shot at this.....
Crossed Flags Emblems - these are the easiest, as they rest in an indented area - are easy to attach in the correct spot due to this. Suggest you fit them a couple times to visualize before removing adhesive backing. MAKE SURE you use the correct one for the location - the hood and rear ones are apparently different.......
StingRay emblems on front fenders - I used blue painters tape all the away around the perimeter of each BEFORE removing the original badges, taking care not to tear/remove the tape when removing the badges. I left about 1/8 inch between the edge of the badge and the tape all the way around. Again, not too challenging to position new ones with this method.
Rear "CORVETTE" lettering - this is, by far, the most challenging as it is actually 5 separate pieces, so you need to worry not only about their position on the car, but their position relative to each other. I again used painter's tape around the outer edge of the whole word - i.e. a rectangle - this takes care of the positioning on the vehicle. The challenge is the 5 pieces relative to each other, and here I "cheated"....I actually did a Buyer's Tour at BGA and watched my car being built. One of the "souvenirs" I got from the tour guide is a foam cutout piece that actually holds the pieces in position so you can apply all at once. This was used when the original, chrome "CORVETTE" was put on my car; but I did not get one with the replacement. So...I "loaded" each of the 5 pieces into the foam template, and attached at once. I have no idea if/where you could get one of these.....
Good luck!