HELP !

I bought the expansion, and can't figure out how to start the expansion section.
This is HUGELY frustrating, since all the "boss" monsters in the basic game have been impossible to defeat - one key example is Dude's quest, since I can't get to the mineral oil without dying 20 times so far...

What do I do to get out of my stuck position and into the new content?

If you're too weak atm to do the Dude's quest, and you can't sneak through the vents, you should probably reload an older save.
You can also try getting one of their uniforms from a locker and see what happens.

The Expedition itself can be accessed through Core City's dock. There's a new area to the east of the dock where the expedition security chief is.

It's a really good expansion, and I'd argue the main quest branch is even better than the base game's main quest. Better writing, and better encounter design.

Killing the Beast in Foundry is another method of joining the Expedition and may be easier for you.

You can also pass a Persuasion check, but the required effective level is pretty high if you've not been investing in it, I think I passed it when my effective level was over 100 but it might be even higher. I started the DLC pretty low at like level 12 or something I think and struggled a bit, returned for a while at level 16 but decided it would be better to come back later, so did everything in the main game before infiltrating Tchort and went back to the DLC at like level 22 and finding it much more managable now.