Hi Jeremy! I've been painting for a few years, and am currently listed in the SAA Tuition tab. I've been running Demonstrations and Workshops for quite a while now, so I pass on a few basics, which are my thoughts alone;
Which part of the country are you in?
I was "discovered" by a Professional Artist who said that I should be doing Demonstrations, so thats one way to get started.
In my experience, once you get started, word of mouth is important, so think about your style of tutoring - make it fun!
Most Demonstrations, though not all, are around 2 hours, so you have to produce a painting, either by demonstration - easier - or by Workshop - more time consuming, as you are going around the members / students and helping them and above all; inspiring them and encouraging them - you have to be positive so that your students are encouraged.
If you have a local Art Group, then offer your services, and ask them what they would normally pay a Demonstrator.
If you want more detailed information, then look at my SAA Website, and contact me, and I'll help as much as I can.
Very best wishes, and good luck!
PA / RSC Wigan / Warrington / St Helens