I completed a CELTA course earlier this year and held a temporary teaching position during the summer. The experience was very enjoyable, and I've since been lucky enough to be approached for private lessons. I'm a little uncertain of how to test for level as this was previously the responsibility of the language school I worked for. Additionally, I'm curious of how others approach the sourcing of materials and lesson planning, and how it differs from classes? The lessons will be conducted via Skype.
Private classes require sensitivity to the demands and expectations of the learner, so getting to know them and being flexible in the early days is important. Some want to talk all the time, so burying them under materials won't work,etc.