Hi - I have a "collection" of CI I use all the time. Oval roasters, skillets, DO's, bakeware, gem pans, etc. All old Griswolds. I use them all the time for cooking/baking.
Hot water is usually enough to clean out and wipe dry for most cases. Set into a warm oven just to evaporate everything before you store.
If you get something crusted on, then simply fill with water and bring to a boil and simmer and rinse clean with hot water, use a green or blue pad works fine.
Dry and apply thin coating of oil as folks mention above whatever your preference will work just pick something mentioned above. You need refined oil/fat with a high smoke point.
I use a paper towel and just spray on canola oil (yep - just plain old PAM). If I don't have PAM I use canola. Wipe good with a folded paper towel. Toss in the oven at 350 for 20-30 minutes, remove and wipe a gain to get of any excess oil. Good to go
If you get very heavy crusted on stuff boil water as above, while simmering take a metal whisk and lightly work back and forth across the rough areas until it clears. You don't have to press hard at all. I have a vintage "scrubber" that looks like chain mail that does the same thing. Empty, rinse, clean as above.
For the minor stick that happens the kosher salt with a little oil to create a slurry works great, but most time I just use a little water.
All of this stuff sounds more involved than it is. 95% of the time hot rinse then the spray and wipe with PAM and oven treatment is all it needs, and a lot of time I skip the PAM after use if I'm going to use the piece again real soon. The biggest mistake a lot of people make is using too much oil. Very, very thin film is all that's needed for maintenance. And often there's enough residual oil to leave a light coat after hot water rinse and dry and wipe down good with a paper towel.
Pretty much the best ongoing conversation around restoring and maintaining cast iron you would ever need you can find here:
Cleaning and Restoring Cast Iron
If you ever end up with a sticky mess or something you just can't deal with you can always take it back to metal by removing the seasoning and starting over. I've never had to go to that extreme once a good seasoning is established. But in a sense that's part of the beauty of CI. You can always bring it back and rebuild the seasoning from scratch and it really isn't all that hard.
I've used peanut oil, Crisco, bacon fat, etc, etc. It all works. PAM is the easiest and provides the blackest seasoning more quickly than others in my experience, but hey it's not a religion, use what you like. Keep the smoke point around 350 to 400 and you should be fine.
HTH