Hi and welcome to the forum.
You're in a position many people find themselves in when they come to Switzerland. Also, as you say, being a native speaker of English and being able to teach English are 2 very different things.
I'd ask yourself. Would you like to make this your line of work here? Then if I were you, I'd look into getting some basic training. There are lots of ways to do this - from attending local workshops to taking a foundation course in English teaching the Cambridge CELTA.
Here is the link for the English Teachers Association of Switzerland. They have regular workshops happening around the regions. I'm the Teacher Development Chair. (and also an accredited CELTA trainer)
http://www.e-tas.ch/
OK - in terms of money - this is a tricky one. On the one hand you have no experience or qualifications so you couldn't charge an average hourly private rate (between 60 - 80chf) but on the other, charging something as low as 30chf is not a good idea as we need to keep a minimum rate. I would suggest 40chf for an hour.
I would probably make it clear that you are going to be conducting a conversation session, where you'll bring in new words and phrases (perhaps write them down in a notebook) but you won't be teaching grammar, language analysis etc. In other words be honest about what you can offer.
If you understand German it makes life easier, you can ask the girl about her interests in German and then as she is talking about them you can thread in the relevant English words and phrases she needs - have her write them down and then recycle them next time. Recycling is essential in language learning. Or you could get a board game and teach set phrases in English - and play together. Again - the element of repetition.
Very easy to teach - label items in the house. Bananas, the fridge, the window, etc. Have her go and stick the correct labels to the various places. You can then continue with teaching what we call prepositions of place "it's on the" it's beside the" etc. Use real items.
Teach numbers and phrases like "it's too expensive" How much is that - through role play - bring pictures of various electronic goods and put price tags on them - first have her practice the expression connected with the pictures, then role play a situation where she can recycle those expressions.
These are just ideas for starters - but really I'd advise you to contact ETAS see what's on offer and go get more ideas and training in your local area.