Hi! Off the top of my head, there have been several different versions of transwarp drive depicted, to varying degrees, on screen.
1) Excelsior's transwarp drive which was only shown to fail when pursuing the Enterprise in 'Star Trek III'
2) Transwarp as breaking warp 10/infinite velocity as seen in 'Threshold' that caused humans to evolve/devolve into small salamander-like creatures
3) Voth (dinosaur species) transwarp as seen in 'Distant Origin' which looked pretty much like regular warp but with longer star streaks
4) Borg transwarp - seems to employ small transwarp coils that allow access to a network of subspace corridors/tunnels that are held up via 'transwarp hubs' as seen in 'Endgame.' The Enterprise-D was also able to follow Lore's Borg ship into a transwarp corridor in 'Descent' without a transwarp coil, I believe using their deflector.
Now personally, I imagine that the first three are all variants of the same 'infinite velocity' transwarp, since there appears to be no corridors/tunnels. I think that the Excelsior just failed to break the warp ten barrier for danger of tearing itself apart, a problem the shuttlecraft Cochrane seemed to suffer from in 'Threshold.' And even though the Voth ship at transwarp didn't seem to be using infinite velocity, maybe it could but was just using a lower form, or different form. (Indeed, lines in STIII seemed to indicate that all warp speeds are, or would have been, had it worked, available through transwarp drive, so it's possible that this just adds warp ten to the top of their speedometer.) One might speculate they use a similar technology that has no 'evolutionary' effects. As to how this type of transwarp would work, I'd say it's anyone's guess but probably a higher quality warp reaction and resulting stronger warp fields, which I believe also had something to do with the Cochrane 'tearing itself apart' in 'Threshold' - the subspace field had deleterious effects on the nacelle pylon structure.
If you're talking about Borg transwarp, theoretically all one would need is a transwarp coil stolen from the Borg, but those appear to have some compatibility issues of unspecified type and burn out after a while. But those also don't have any specified side-effects. You would of course have to steal a coil from the Borg.
You could alternatively use quantum slipstream drive, which at least looks the same as Borg transwarp, and Voyager couldn't quite make work either, but has been suggested in the novels of late that Starfleet has been playing around with in the post-Voyager return timeframe.
Hope that helps!