If your distribution (like Ubuntu) supports it, you can double click on the file to start the installation process.
If you do not have a graphical installer or would rather like to install it via command line, open a terminal and navigate to the folder where the .deb file is located and invoke:
# this command will give you an error, please ignore this as it will be fixed in the next step
dpkg -i <anydesk.deb>
# this will fix the error above
apt-get install -f