Training comes in three areas of focus.
Safety: You don't want to shoot yourself or anyone else or anything else that you don't intend to shoot. You also don't want to get your thumb caught in a spring-loaded slide, etc.
How-to: Maintenance of the gun. Cleaning, function checking, malfunction diagnosing, how to shoot, how to draw, how to carry how to store, good shooting technique, combat tactics, preparation (both physical and mental).
Legal: Where and when can one carry? What do do after a firearms-involved encounter (whether a shot was fired, gun displayed or just mentioned - I know someone who was arrested and tried criminally for simply, and I quote, "offering to shoot out a car window" and displaying (maybe) an air pistol). The after-shooting consequences. What to say to the police. What do do when the police arrive (you don't want to be shot by a first responder). Do you have liability/homeowner's insurance that will help with civil suits, should one occur?
A fourth item: Moral implications. Are you mentally prepared to use deadly force? How do you intend to deal with the post-incident (shots fired or not) stresses on your psyche and mental state (post-traumatic syndrome)?
On top of those considerations, it is a good idea to plan ahead how NOT to be forced to use a firearm. But this is a good idea to plan whether you carry a deadly (or less-than-lethal) weapon or no weapon at all. Avoidance, prevention, defusing of threatening confrontations is almost always a good idea.
There is a standing piece of advice about driving instruction (which can be overcome, but those who can overcome the difficulties are rare): Do not try to teach a spouse how to drive. There are too many interpersonal dynamics involved in emotional relationships that affect (and often interfere with) the student/teacher relationship. Learning from friends or people in the business of selling goods is iffy. Learning from experienced instructors is better. A teacher is master of two arts. That which is being taught and the art of teaching. If you want to learn well, don't short-change yourself. Get the best instruction you can.
How much training you take is up to you (some local and State laws may infringe on your autonomy in this decision, but you get the idea). (edit: with a nod to JimBob86, I am not recommending requiring any of these, but recognize that some jurisdictions already do.)
Learn Safety first. Most How-To courses will terminate your class if you are not safe, especially the ones teaching tactics.
Learn maintenance next. If you cannot take care of your gun(s) it(they) will not take care of you. A poorly maintained gun is likely to malfunction.
If you skip either of these, don't own a gun. Don't even pick one up, absent some overriding emergency.
Legal knowledge is HIGHLY recommended before carrying on a regular basis. You don't want to guess, "shoot, don't shoot" during a confrontation.
Tactical training is advisable if you want to give yourself the best chance of coming out of a confrontation (on the street, and later, in court) on top. Hitting a bystander during a good shoot is bad news.
Moral, psychological aftermath. If you are mentally prepared beforehand, you are better prepared for the inevitable aftermath. Ask any combat veteran how even the best preparation is never enough for the first time you kill or wound someone.
Medical (first-aid) training is a good idea, too. Once you have shot someone and ended the threat, you, as a human being, are generally encouraged to save the life of the whoever is injured, whether it is the bad guy or someone whose life you saved by shooting the bad guy.
Thanks for reading. Pardon my rambling.