The best options (IMHO) are taking the Amtrak and/or Metrolink to the Fullerton Station, then taking the OCTA bus, Route 43 to the Disneyland entrance.
There are some issues, first is the timing, Metrolink is cheaper, and will give you free bus fare by showing your ticket than Amtrak. But Metrolink has limited hours. So for most folks, Amtrak is better, but even the last Amtrak prevents you from seeing the fireworks.
I prefer Fullerton for a few reasons, it is quicker (one less stop than Anaheim from Union Station) and much easier to access the OCTA. Also it is cheaper for many fares.THe bus takes about 20 minutes from Fullerton to the DLR entrance.
Just say NO to the Anaheim station, unless you are going to use the Metrolink Trains in the AM on weekdays, as they do have a bus that goes to the DLR from the station, or use the ART system.
Most of the time, you need to take a LONG walk from the station to Katella Avenue to catch the OCTA route 50 that goes down Katella and stops in front of the 7-11 at Harbor and Katella, and a good walk to the Disneyland entrance after being dropped off.
Woodland Hills CA - Hottest spot in Los Angeles City Limits
Re: Best route from Union Station
There's the L. A. Metro 460 bus that goes between Downtown LA and Disneyland - it will take one transfer to get to it, either the Metro Red Line Subway or a dozen different Metro Bus lines cross paths with the 460. But there isn't a really "late" bus back, if you want to spend the evening to watch Fantasmic! & fireworks you can't get a reliable bus home at closing time - you might want to find an inexpensive room and stay overnight.
(* Do NOT bet your life on taking the Last Bus anywhere. If the last bus breaks they might send out a replacement to sweep the route and get everyone home, but they might not - even if they do, you may miss the next connection. The "Commuter Express" buses are notorious for both frequent breakdowns and abandonment.)
You can take the train - Amtrak Pacific Surfliner to Fullerton, then the OCTA #43 bus to Disneyland.
There's even Greyhound or Airport Bus or Supershuttle... A million different ways to do it, pick one. Myself, I just drive it, but around here we're wierd that way.
I think it actually is possable... It CAN be done... The question is, do I really want to try this kooky idea I have?
We still don't know what that "kooky idea" is; we've just been asked questions about transportation from Union Station in downtown L.A. to Disneyland, without explaining when / why / how / what... and you've received a half-dozen (very nice, very informative) responses.