Okay now this is a question that I truly feel qualified to give my two cents on. I have been a comic book reader as well as a collectables dealer for most of my life.
Where to start? Well, assuming you're not rich let's begin with graphic novels and bargain books.
Graphic novels(GN) contain either done in one stories, complete series, or story arcs from longer series. They are a great way to start since you get a whole tale in one easy, carryable format.
Bargain books are available in most comic stores. Overstocks, last ones, not selling in our area, etc. Depending on the title and store you can new comics from a quarter to a dollar each.
May 2nd was Free Comic Book Day at comic stores across the US. To promote and generate interest in our pulpy world. Although the day is gone, the celebration goes on. Most stores will have deals all month. Many owners will give an instant discount too depending on purchases. Especially if they know you're new. It's not the poor economy. They are genuinely nice folks at heart.
Don't be surprised at the tripe you encounter though. Unfortunately some comics give us fans a bad name. But on the other hand, comics are not unfamilar with the Pulitzer Prize either.
Both options above are great ways to introduce yourself to comics reading. But you must get your hands inky! No online buying just yet! You must read the blurb and flip thru the artwork. What catches your eye? It might be something you never heard or thought of.
Tie-ins are a good way to break in. I think that was mentioned by someone earlier. Almost every TV show, cartoon, radio series, serial, celebrity, movie, book series, or current geek (myself included) fad, has had a comic book at some point. From Howdy Doody to Walking Dead.
A couple of my favorites are Ellison's Demon with a Glass Hand and Matheson's Hell House. Matheson himself praised the adaptation. These are older titles. You may have to hunt if interested.
I only ask one thing of you. When you're done reading, if you do not want the books-recycle them please. To other readers. Donate to charity-tax write off! Schools-anything that keeps kids reading. Age apropriate though! Or my personal favorite is donating them to our soldiers overseas. They are desparate for stuff to do during down times. They are bored and miss home. I do not have the info handy, but if anyone is interested I can find it for you.
I hope this helps a little bit to you. And others! There should be no stigma about reading comics. It's certainly not in Japan! Comics are just a tale with pictures added. Isn't that called an illustration in a novel?
If you need any other advice just ask-I, no scratch that. WE are always here to help!
Jack-I'm so jazzed up that I'm going to pull out some comics from my collection right now!