What device are you using it on? I am not sure about the very recent
versions of Android, but in the older versions the logs are saved in the
"logs" subfolder within the "xcsoardata" folder at the root of the main
storage area. That xcsoardata folder is also where you (or it) put your
map, waypoints, and configuration files.
You can use a "file manager" type app (a simple one comes with Android),
or the file selection browsing capability of a web browser app, to find
that folder and handle the log files. E.g., copy them to a flash memory
device, attach them to an email, copy them to cloud storage, whatever
suits you.