Before I tell you how to do this, I just want to make sure you know that watching something online that is longer than 15 minutes can seem like an eternity to the viewer, especially since other distractions are very easily accessed on a computer. When I open up a video that is longer than 10 minutes, I really evaluate if I'm up for this type of commitment. If possible, chunk your content down to 5-10 minutes. That said, sometimes there is a reason to have a longer video.
To increase your time limit, go to the Upload page on YouTube (in the yellow box below).
Then click "increase your limit" toward the bottom of the screen. You will be asked for your number and sent a text with a verification code, which you will type in to the next screen.