What you need: empty PB jar, coffee cup, sandwich bag, spatula (flexible), dish washing soap, a dish scrubbing pad and a pan.
Step 1: Get All the PB That You Can Out of the Jar
Put the sandwich bag in the coffee cup, with some of the bag over the top rim of the cup.
Use the spatula to get all of the PB (that you can) out of the jar.
Scrape the PB off the spatula into the sandwich bag, scraping it on the rim of the cup.
Note that there is a small ridge/lip at the very top of the jar - use a corner of the spatula to get the PB out from under it.
Step 2: Add Soap and Heat Water
Almost fill the jar with water. Pour the water into a pan. Put the pan on the stove and heat the water.
Put about a teaspoon of dish soap (I use Dawn) in the jar. Put the jar in the sink.
When the water simmers, turn off the heat. Wait a minute (or 2) for the water to cool just a bit. Pour the water into the PB jar (this is why the jar is in the sink).
Notes: You can clean the jar with 'just' hot water from the faucet, but the really hot water really softens the PB. You can pour boiling water into a plastic PB jar (yes, I've actually done it) but the jar gets very soft. You can NOT put the jar with water in a microwave and heat the water. The microwave disfigures the jar!!
Wait a minute or 2 (because the water is HOT) and swirl the water and soap around the jar. Put the lid on the jar and swirl the soapy water around the top.
Step 3: Clean the Jar
Wait a bit for the soap and hot water to dissolve/soften the PB and cool a bit.
Use a dish washing scrubber (scrubby) to clean the inside of the jar and lid. Use the handle of the spatula to rub the scrubber on the bottom of the jar. Don't forget the little ridge at the top of the jar.
Pour some of the soapy water out and tip the jar to see if any PB is left. Scrub it off.
Pour out the soapy water and rinse the jar and lid.