First, figure out which events you want to attend by checking the Inaugural Committee's Official Schedule. Sign up at the PIC's mobile update site for text alerts of news updates, weather and schedule changes, etc.
The Big Three are all online with free streaming coverage. NBC's coverage is over at MSNBC's inauguration page. CBS' Inauguration webcast goes all day, ending with a web-only wrap-up hosted by Katie Couric at 10 p.m. CBS' coverage is on Joost's Everything Obama site. ABC News is hosting live coverage at its 44th President site.
C-SPAN's main page features a kind of "control room" that lets visitors switch between four feeds of the goings-on on the fly.
Twitter is providing real-time tweets/updates you can follow by searching keywords like #inauguration or #Inaug09. Perhaps the cleanest, most easy-to-follow interface is provided by Deep Focus whose Tweet the Inauguration provides one at a time updates, like a slide show.
Also offering free streaming coverage are the Washington Post, New York Times, and the BBC.