This is pretty much your only public transportation option.
Take the Metro Express Bus 460 from Harbor Blvd/
Disneyland East Main Shuttle ENT (SW corner) to Figueroa St./Wilshire Blvd. (NE corner) the fare one way is $2.25 and the express makes few stops (including Knotts Berry Farm if you want to go there, this would also be the bus to take).
Then you'll walk to the 7th St. metro Center Station (not sure where it is exactly, I'm going by a website, but I think it's near that intersection, the bus driver would know), and take the Metro Red line to North Hollywood Station heading west line (there's two red lines there) and you'll get off at the Universal City Station (walk across the street from the exit and take the free shuttle up to USH). The metro ride will cost $1.25.
Here's the catch, you'll be limited to what times you can leave and arrive, and the whole trip will take you up to two hours on heavier traffic days. But that's the cheapest way to get to Universal from Disneyland.
Here's the LA transportation website.
http://www.mta.net/default.asp Just type in Disneyland and Universal Studios in the search section, and fill in the other fields, you can also surf around on the site for other options.
Hope that helps. Although it's not ideal, the public transportation system out here is not terrible. I wouldn't ride it by myself at 1am, but during the day it's pretty safe.
If it were me, I'd go Greyline's direct bus or get a rental car for the day.