I'm changing out the trunk badge on our 1973 Ford Mustang Convertible here, but really this could apply to just about any of the old pin-type badges on just about any car. I know it's extremely simple and you could figure it out yourself, but here are a few tips on the process.
The first thing you have to do, if it isn't missing already, is to remove the old badge. You can see on ours that the "g" has broken off. It's really not a big deal, but it was bothering me and it's a very cheap part so I had to swap it out. Pulling these badges out isn't difficult or complicated - you just pry it away from the body until it pops off. This particular badge has three pins. My only tip here, and it's a really big one, is to tape all the way around the area to protect the paint. I used painters tape, but masking tape works fine. I simply used a flat-head screwdriver and very gently and patiently worked the badge away from the body at all three pins until they came out.
I got my replacement part from CJ Pony Parts - one of the many Mustang parts suppliers on-line. I went with a Scott Drake aftermarket piece. It's a little cheaper than an NOS, and probably better quality. It fit perfectly and everything lined up with the original holes. It also came with the three tube nuts (as they are called) as well.
I probably could have reused the old tube nuts, but since I had new ones I just pulled the old ones out. It was a little tricky, and in fact one of them actually got punched into the body but it's so small and light that it won't make any noise or cause any other issues. Basically, you are just distorting the old nut until you can pull it out with needle-nose pliers. Simple, but it's important to be careful of the paint.
Putting the new tube nuts in is extremely simple. You just set it in and tap it with a hammer. I opted to use the thick and soft packaging the emblem came in and a small rubber mallet. It doesn't take much, just a light tap and it will pop in place. I did the same thing to pop the emblem in place.
There you go - better than new. This is about a 10 minute job, and about 7 minutes of that is taping around the old emblem. As I mentioned, this was our trunk emblem which is about as easy to work on as it gets. If you have to do a fender emblem, you will be on the ground and might have some funny angles, but it's still a simple and quick DIY project for your car.
As a general rule, everybody is going to check out your rear end so you might as well make it as presentable as possible.