Sailfish OS supports several ways of capturing pictures from the device display.
1) Press the Volume Up and Volume Down keys down at the same time, and keep them pressed for a second or two until you hear the camera shutter tone and/or see a notification banner appear at the top of the screen with text "Screenshot captured".
The pictures are saved to folder Pictures > Screenshots. They can be viewed in the category Screenshots of the Gallery app.
2) Another option is to install screenshot app from developer 'lbt' from Jolla Store. This app allows you to take screenshots with a delay of 3 to 15 seconds. There is no 64-bit version of the app, though, so it is not available for Xperia 10 II or Xperia 10 III (status on 2021-12-01).
This app saves the pictures to folder Pictures > screenshots (note the lower case s as a difference to the other tool).
DISCLAIMER: This app does not work on Sailfish 4 due to the additional restrictions caused by app sandboxing. Hopefully, it can be fixed.
Also, in this case, the pictures are saved to folder Pictures > Screenshots (unless you change the path on the last line of the command).
devel-su -p dbus-send --session --print-reply --dest=org.nemomobile.lipstick \ /org/nemomobile/lipstick/screenshot org.nemomobile.lipstick.saveScreenshot \ string:"/home/defaultuser/Pictures/Screenshots/Screenshot-$(date +%y-%m-%d-%H-%M-%S).png"
(please note that each line of the 3-line command above is separated by a space character)
NOTE: Sailfish OS does not support capturing video clips.