If you haven't thought about it, are you sure you want to? It's not a decision to be taken lightly. If you buy a gun and stick it in your pocket "just in case" without really thinking this through and without taking the time to really STUDY the law, carry options, tactics, etc... Well then, if something happens, you might just as well hold the gun to your own head.
Beyond that, do you already have a handgun? Do you have one that would be suitable for concealed carry? Do you have experience with semi-autos and/or revolvers?
A lot of people nowadays seem to want to immediately go to a semi-auto, but unless you're willing to spend a lot of time at the range learning how to clear jams and operate it you're probably better off with a simple double-action revolver. And the sad fact of the matter is that if you aren't already in the habit of going to the range every other week or so, it is highly unlikely that you will spend as much time learning your gun as you should--even if you sincerely intend to.
For someone who is a newbie to handguns, my advice would be to start with something like a S&W Model 60 with 3" barrel. It's small enough to be pretty easy to conceal, yet large enough to be controllable and easy to learn with. It shoots .38 spcl, which is a perfectly adequate defense round, and can shoot .357 mag if you work up to that.
To get started with handguns I would recommend taking at least one beginner pistol shooting class. The NRA has instructors in many communities. You might start by contacting the local police or sheriff's departments, since these classes are often taught by law enforcement officers.
In Colorado to apply for a conceal carry you must successfully complete at least one NRA sanctioned class. I'm guessing other states have similar laws.
In Washington you fill out the forms and pay the fee at the sheriffs office. They do a background check and two weeks later you get a permit in the mail.
I did hear something about future changes in the procedure.
I've spent countless hours either on my hands and knees or bent over, messing up my back, looking for blood. One such instance I remember most was a hog hunt a few years ago in Mississippi. I had never shot a hog so when I poked a hole in this guy; I was determined to find him. Wearing snake leggings, I crawled on my hands and knees through the briars and the brambles and bushes where a rabbit wouldn't go. I found a spot of blood here and there but never the pig. And lucky for me, I didn't find...