In fact, it's pretty easy, but I'm married in the Southwest, so just for your reference.
First, you may find a family clinic to get both your blood tested, so you would plan to save half a day to do that. Second, after you get this done, you may start to plan for the date you wanna get married. On that day, your big day, don't forget to bring your driver's licenses and dress up (you might not need a wedding dress or a tux, but you can let yourself look good if you want to, or jeans are acceptable). And then, bring your rings (and flowers, maybe) and 2 witnesses--you would need their signatures. When you are ready, go to the district or your city's court and ask for the marriage license office and then buy one license--it costs around US$35, and extra $6 for one or two copies (I can't remember). The staff at the marriage license counter would schedule the time for you and have you be back to get the license after vowing at the court. Then you guys are all set!
Let me know if you need more info...