It says on the tails website that the usb-stick installation of tails can be corrupted if you install it from a compromised system. I installed tails on a usb-stick from my windows10 pc. I have no idea if my windows has been infected or compromised, my malware scanner doesn't show anything, so how will I know that my usb-installation hasn't been corrupted?
Depending on how the USB was created, you may be able to checksum the raw data that was written and verify it is the same as the expected ISO from a different computer or operating system.
I don't think Windows currently creates the USB in this way but if it was created using the
dd utility from linux, for example, you'd be able to check the written data matches the signed ISO. However, there is no way to verify this from a compromised system. That is a chicken and egg problem, any tools you run could be tampered with on the compromised system.
The best heuristic method for this is to gain multiple, independent positions of observation. If you download and verify the ISO, then write it to the raw block device (e.g. using
dd on Linux or UNIX) then verify the written data against the expected signature on some set of available and distinct computer systems, and they all agree that the written data and signature are a match then you're probably about as safe to proceed as you could realistically expect, at least as a non-expert.
There are limitations on what Tails could protect against, certain types of compromised system will never be safe to run Tails on even if the installation of Tails itself was not tampered with, please read the Tails warning page.