You can make your way to either the Anaheim or Fullerton Amtrak/Metrolink stations and take either Amtrak or Metrolink to Los Angeles Union Station. Once there, you'll take the Metro Red Line to the Universal City station which is just right down the hill from USH. It'll probably take around two hours.
SoCal Gray Line do packages with bus there, USH walk in entry, bus back. You can also choose a scenic night tour of LA on the way back sometimes. I took the there/entry/back package last September, USH closed early for their Halloween decorating that day so the LA night tour wasn't available.
I was disappointed with USH*, but the bus service was good.
*(A lot of attractions were closed, it took me about 3 hours to do everything available and even then the Waterworld show was cancelled 5 mins in because they turned over one of the boats, the rest of the day I hung out in the Irish Bar drinking frozen margaritas... USH in Sep is a waste of money).
Disney FAQ#275: What is DCA?
DCA stands for Disney Construction Area. All the Cast Members are themed with hard hats and steel toed boots.
You take the 460 on Harbor Blvd. to Norwalk station. Then you transfer to the Blue line, You get on the Red line and get off at Universal.
But these are not the safest areas.
1. Norwalk Station is where one gets on the Green Line. Green Line to Blue Line to Red Line.
2. Taking a cab to Norwalk might be faster. The 460 takes at least an hour to get to Norwalk from DL, taking a very non-straight line and stopping a lot. After Norwalk, I believe it is non-stop to downtown, subject to the whims of traffic. Then more stops downtown until 7th Street Metro Center, where one can get on the Red Line to Uni.
3. As has already been reported, USH is a big fat "Meh." I'll take a beach trip over it, and I often do (but then, I live here).
4. The trains and stations are a lot safer than a block away from them. Best not to take any money, except for train fare. Get a whole-day pass. Safety risks increase more with exposure.
OP, spend the whole day in the USH area. Trains run late. Get the most out of it. City Walk has some great places, such as Howl at The Moon, which has Dueling Pianos taking requests (for a price).