When cleaning:
Wash with soap and water after use. Soap is fine for cast iron.
Dry thoroughly after cleaning.
Warm on stovetop until warm to touch.
Apply a light coat (literally, drops - more than that will burn on the pan) of a high smoke point oil to cast iron. Wipe away excess.
When cooking:
Cast iron is non-stick. Heat the fat you’re cooking with in the pan as the pan warms. Make sure to heat both well before you place food in the pan.
Cast iron gets very hot - there are very few instances where you need to heat the pan past “medium” heat on the stove.
Any utensil or spatula is fine on cast iron.
Seasoning
You can use multiple different types of oil to maintain and season your pan. My suggestion is a high smoke point, neutral oil such as grapeseed or avocado oil.
If you want to take your seasoning compound to the next level, I'm a big fan of Cast Iron Chris' seasoning compound. It's a thicker, waxier consistency that applies to the pans very well.
Cleaning Tools
A chain mail scrubber can be a very useful tool for scrubbing off stuck on food. Something like this chain mail would work well.
Utensils
Any utensil or spatula is fine on cast iron. I generally use wooden spatulas and spoons most frequently in cast iron, but also steel spatulas are effective as well. If you're using a plastic or silicone utensil, be conscious not to leave the utensil on the pan as it will melt onto the pan.