What photo editing program do I need to cut-copy-paste from one image to another?

You can do that with Paint. I used to do it all the time.

There isn’t really a program that will let you click a few times and be done. You are going to have to buckle down and learn how to do it and it will take a long time. It is easily doable in the Gimp if you are willing to spend the time to learn.

And by spending time I mean like a hour.

You need to learn about layers. It is difficult to start. When you understand, you will be amazed at your skills!

This might help:

Tutorial to Swap/Combine Faces in GIMP

And here is a funny story about how I learned to use Photoshop. My sister has a odd thing for boobs without nipples. So she would pay me when I was in college to use photoshop to remove nipples from images she found on the internet. She paid and Rule 34.. I have no idea.

Adobe Photoshop is a very comprehensive program for this type of work. Gimp is also another as you have found out. Each program will have it’s own learning curve and it is up to you to practice and experiment with the tools that each software package provides in order to yield the best results. As others have mentioned, learning how to use layers and masks will also help you tremendously. Practice with smaller files and go through some tutorials like: http://www.technorms.com/36067/swap-combine-faces-using-gimp or https://www.youtube.com/watch?v=T2q7D-8uAbQ.

@DrasticDreamer I really can’t use Paint, struggle so so much, guess I just have to practice a bit more hey. But finally I just gave up and now I just ask someone that can when I want to edit a picture. @NuclearWessels try Photo Pos Pro, I haven’t used them much as I haven’t had the need to edit, but they give you a step by step on how to with pictures, might help: http://www.photopos.com/Photo-Pos-Pro-Free-Photo-Editor.asp