How do you jailbrake an iPhone the safest way that it won't get messed up?
Jailbreaking is safe to do. If you have any problems and or are unhappy with it just connect to iTunes and restore your phone either from a backfile you created or back to factory Do a google search you'll be enlightened
There is no safest way to jail break an iPhone. It is illegal and could void your warranty. If you still want to do it pick the most popular programs.
Like @brandenhouston said there is no safe way to jail break an iphone. It is always done at the discretion of the iphone owner and voids your warranty once it is completed.