You can upgrade your pledge by clicking on the "Manage your pledge" button on the upper right corner of the landing page for the campaign. From there, Kickstarter will take you to a new page that will allow you to do a few things like change your payment method etc. There's a "Change your pledge button" near the middle of the page. When you click on that, you're presented with all of the pledge options. Select the pledge option you desire and Kickstarter will update. And, that's it. You're done.
.....Thanks to Travis Mueller for getting this answer together for us!