@Carsten: welcome to the club..
EFHW antennas: I built several and I've been helping local OMs with building and measurements. The first step is to acquire an off the shelf one or to build DIY the EFHW antenna. Before the tuning the antenna has to be completely assembled inclusive transformer in a suitable box, coax, connectors, etc.
The next step is to "tune" the antenna - that is the very moment the nanovna comes handy.
An EFHW for 80-10m with 110uH coil for 80m band will fit inside your garden, as it is aprox 22m long system.
The antenna uses a ~110uH coil after the first 40/20/15/10m segment (aprox 20m long), then another aprox 2m length of wire for the 80m band.
You first tune 40-10m band by changing the length of the first aprox 20m wire, then the 80m band by changing the length of the 2m piece of wire.
You always cut the lengths longer than required (the swr minima below the required frequencies) at the beginning, and then you slowly cut off small pieces of wire while you watch the minimum of the SWR on your nanovna on each band such it fits your bands as best as possible.
All you need is to connect S11 of your nanovna to the antenna coax and watch the SWR at the bands frequencies.
There is a lot of guides on the web available how to make a good EFHW antenna!
A great learning exercise for a beginner, indeed!
