Below is the rough suggested installation procedure, a quite detailed video is available as well. If you are doing manual partitioning during the process it is advised to create the partitions with Gparted (find it in the start menu) prior to starting Calamares (installer) as it is a known problem that more complex partition layouts might not get created properly. If you have a MacBook pro, we have a dedicated wiki article which helps with the installation!
Check if hardware requirements are met. Read this wiki page for this purpose
Download your desired edition and the fitting .sha256 file from the downloads page. If the direct download is used you can copy the link and the following in the terminal:
Verify the checksum of the downloaded ISO to see if the download was successful, use in the same directory:
sha256sum -c file.sha256
Burn the ISO a USB thumb drive of your choice. Recommended is DD since it's working most of the time, unlike other methods. It's very important to check where the thumb drive is located in the filesystem prior to doing the actual dd command. Replace /dev/sdX with the actual location of the thumb drive.
sudo dd if=file.iso of=/dev/sdX
Boot the created installation media and follow the instructions of Calamares to install Garuda to the hard drive. It should be self-explaining, otherwise, there is this video showing the rough process. If you need help partitioning there is this Arch wiki page containing useful information on it, for dual booting with Windows information can be found here.
If the installation completed successfully Calamares will offer to reboot the device. Garuda Linux is now installed :)