Blast it down with a can of engine degreaser and let it fully dry. You should be able to hear the faintest rattle in the links if you shake it. Lay it out with the plates on end, and apply a drop of lube to each roller, flip it over and another drop to each roller. Move the chain around to work the lube into where it needs to be. Depending on the type of lube wipe away the excess (oil) or try to let it dry for a day before wiping (suspended wax). There should be no residual oil on the plates, it should all be in the rollers.

I just soak it in some degreaser or iso 90 and then wipe it down, let it dry, then lube it with my ceramic lube.

I use Silca Strip Chip along with their wax, plus Endurance Chip. No more bullshit. Especually in dusty environment, if affordable, wax should be great.

Chain wear sticks have two measurements normally - if you are beyond the longer one, you may find that your rear cassette is worn too and that your new chain skips. Hopefully you're fine though.

I have an old tupperware that I put degreaser in, stick the cassette and chain in there, wash, rinse, put on bike, then oil.

I use a foam degreaser to get the factory stuff off and then yeah, just normal chain lube, wipe off the excess afterwards just like when you clean your chain

If your chain was that bad you almost definitely need a new cassette (back) and maybe even a new chain ring (front).

My lbs recommended WD-40 too. Works for me.