It's actually a really, REALLY tortured process. Not Hawkman/Donna Troy bad, but still really funny:
Pre-Crisis
There was an Earth-Two version of Green Arrow and Speedy. They were members of the Seven Soldiers of Victory. The whole team was tossed around in time when their unofficial "8th Soldier", Wing, sacrificed himself to save the Earth. They were eventually rescued during a JLA/JSA team-up, which notably included the Earth-One Green Arrow, who was amused to discover that he had a doppleganger.
Most of the Seven Soldiers, now dragged to the present, were rarely seen over the next few years. The Star Spangled Kid became a member of the JSA and Infinity Inc.. The Crimson Avenger died. Sir Justin went back in time to Camelot. There was a funeral for Lee Travis. And that was it until...
The Crisis
During the Crisis, the Earth-Two Green Arrow was explicitly killed as part of the "giving the dopplegangers one last hurrah" spree that happened during the story. Amusingly, the Earth-Two Speedy isn't given a similar send-off. Poor bastard.
Post-Crisis
In the Post-Crisis Clutter-Earth DCU, there never was a "Golden Age" Green Arrow or Speedy, as the one and only versions of these characters made their debut in the modern age. This leaves a hole in the Seven Soldiers of Victory, who by nature of their name kinda sort need, y'know, seven members. This hole is filled in various ways over the years: Sometimes Wing is a full Soldier, along with Vigilante's partner, Stuff. Sometimes Vigilante's other partner, Billy Gunn is added into the mix. One telling has the Shining Knight taking on a sidekick of his own in the form of a Golden Age Squire. Oh, and TNT and Dan the Dyna-Mite were retconned in at one point. One of the more enduring retcons that eventually sticks is sliding Alias, the Spider (an old Quality Comics character) into Green Arrow's role (he's also eventually revealed to be a secret villain, but that's a whole 'nother kettle of fish.)
For my money, none of the retcons were particularly bad, but none of them felt great. This goes on for some years until...
New 52
Golden Age? What's a Golden Age? Everything's new and now! Check out these collars, baby!
Sorry. Let's fast forward to...
Right now
It's revealed that there was Golden Age Green Arrow and Speedy who joined the Seven Soldiers of Victory, and they were (ta-da) the modern day Green Arrow and Speedy, spending some time stranded in the past due to Time Travel Shenanigans (as one does).
This, to me, is a perfectly cromulent retcon. While it probably means that a chunk of the Golden Age GA's adventures have been compressed/eliminated, it "restores" the original line-up of the Seven Soldiers, opens up some interesting storytelling possibilities for Ollie, and is good solid comic book fun.
I kind of hope that when the JLA/JSA rescued the Soldiers in this continuity, modern Ollie was confronted by the fact that eventually he had to go back in time and wear a funny costume. 'Cause that's funny