How to help someone with dementia understand how to spit/how to encourage them to spit?

You can't get them to understand how to do anything, as your client is obviously way past the stage of being able to understand the spoken word, so save yourself the time and trouble and just have your clients family order the Xylitol gel that Lealonnie recommended below, and just forget about the mouthwash.

Use toddler toothpaste so that if they swallow it, it's not a problem. Don't use mouthwash unless it's for children.

You cannot get her to spit, so stop trying.

What is the best toothpaste for dementia patients?

Xylitol Gel – Also made by AllDay (Elevate), this gel is a toothpaste made of 44% xylitol, has a great taste, and is meant to be swallowed. This has the consistency of toothpaste and also picks up food particles. This is a great recommendation for those whose patients tend to swallow their toothpaste while brushing.

Several brands of Xylitol toothpaste are available on Walmart.com

https://www.walmart.com/ip/Brilliant-Toothpaste-Gel-by-Spry-With-Xylitol-Fluoride-Free-Mint-Free-Safe-If-Swallowed-Natural-Original-3-oz/1271169807

You need very minimal amounts of toothpaste on the brush; it is the soft brush that should be doing the work. That will limit the amount of spitting required. Discuss with a dentist what is the best dentifrice to use.

This is very very common, this inability to take in instructions, compute them, and follow them. What you are seeing is common. Discuss with other caregivers. Use youtube videos; you can find almost anything out there and in fact there is one called "conscious oral care" and many others.
I highly recommend youtube. Just type in youtube and you interest such as "oral care for seniors" and you will have videos to help you. They discuss everything from turns to teeth.

You are a caring caregiver and I commend you for that.