.... my problem now ist how to connect ist to vga. anybody with a very simple solution for an absolute beginner? 
first, welcome here.
second, there is a simle answer, you can´t 
Galaga´88 is a 15K lowres game, it doesn´t output VGA signals.
The only solution to use it on a VGA monitor is to hook up additional devices, like a cga2vga scaler and a sync splitter. And of course a SLG3000 for the scanlines. You can check out Bencao74´s website for more info about that.
But please don´t use thta equioment, you don´t really want to use a VGA monitor. The game is intended to use with a 15K monitor, so why not hook up one of those?
But to be honest, I am a bit amazed that you thought that you could hook up a Galaga ´88 PCB directly to a VGA monitor! Obviously you didn´t do a lot of research on forehand.
i did no research at all when i bought the pcb but of course I knew that the galaga 88 has no vga-out. i just did not think about it when i found it on ebay and bought it. actually I did send the guy a price I was willing to pay.... and he accepted one minute later. so... there was my galaga 88 pcb.

the reason for me to connect it to vga is simple: i have no other choice at the moment because i have a coctail cab (not a sitdown as mentioned before). i bought this cab with a 60in1 two years ago because I liked its design. it did fit in our appartment and it was a compromise to my wife. she liked it too cause it was a piece of furniture for us. unfortunately it came with a vga-monitor.
i could of course put a real 15k monitor in it... but that´s something I might to in the future. at the moment I don´t have the time for that. I just want to play that game again with a beer next to me in my livingroom.

so I guess I will go with this little box and the scanline-generator. that will do for me. if i ever have the chance to get my hands on dedicated cabs for my own real arcade i can assure you that I will only go for the real thing.