How do you thoroughly wipe a computer?

I have two old computers that I would like to get rid of or donate however; I’m concerned that credit card information or personal information or pics may still be on their that someone can bring back if they know how to do it.
I’ve read about several programs or ways of doing it on the web but I never know if it really works since most are about selling their product. Of course they all claim to be better than any other way.
I would appreciate first hand information on any products flutherites have used, that they know for a fact is effective.
I don’t need anything to save my information. I have already done that long ago and saved important information or pictures to my removeable hard drives.
Just need to wipe it so I can give it to charity without worrying about the wrong people getting a hold of it.
Also I have one computer that totally crashed. So how do I get that one to run so I can clean it? Would I just be better off taking it apart?