The rate may be market-driven, so I'd check out local rates for 1/2 hour lessons at mom n' pop music stores that offer them or post teachers' ads on the for hire/to gig message board, classified ads, maybe even your town's Parks & Rec Dept offers them.
As for what you should know... that's a tough one. Your approach/syllabus may depends on the age of the student, and somewhat on what types of music she may like to learn to play for relevance to hold motivation. If you don't have a plan, you can go with an off-the-shelf set if texts like the Hal Leonard series, if nothing else, for your own guidance, to steal ideas from for a framework to customize/personalize.
Regardless of either of those factors, besides teaching the elements -- names of the parts of the guitar, how to tune it by ear and/or by machine -- you'll need a metronome, to keep an accurate pace and to develop the student's internal clock.
Also, hand them a $2 foam stress ball to use as a finger/hand exerciser they can use when they're sitting around reading or watching tv or riding in the car. Don't have them waste money on some POS like a GripEase. Those are gimmicks. Tell them to buy 2 sets of strings instead.
And regardless of your syllabus or the music style, I always started kids off with a set of fingering/picking hand exercises to warmup with. Maybe you have one? I have one I didn't learn until I'd been playing almost 15 years, and when I was turned onto it, by a player 20 years my senior, I wished I'd known it from the start.
This absolutley needs to be the first 5 minutes of every lesson, and of every 'take home lesson'. Essential to developing good control of the right muscles and muscle memory in the fingers, hands, wrists and forearms, as well as coordination of the 2 hands. Stress the importance of the benefits (rewards) of slogging thru at least 5 minutes a day of these, that doing these will make the journey easier to navigate. Tie the exercise in to a couple of simple licks relevant to their taste in music as a dangling carrot.
If the kid doesn't buy into these, and you'll see this clearly after the first 2 lessons, drop them. Fast. Don't steal dad's money and don't waste your time. They don't care enough. If they 'get it', if they really do want to learn, they'll take you up on the dare and get with the program.
^^
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