Getting Started RPI2/3
You should be able to extract the zip file by right clicking in the .zip file and clicking in "Extract", "Extract Here" or any variants of these using your file manager.
For windows, there are plenty of tools to help with extracting zip files if the built-in file manager does not work. 7zip is an example.
For Linux command line:
By design, the image is made so that installation is simple. All that is required is dumping the image to the sdcard. To do this with Linux:
sudo dd if=Manjaro-Arm_[Edition]_rpi2_[version].img of=/dev/[device] bs=4M
There are tools and GUIs that can make this process a little easier such as Etcher and instructions for those are included with the respective software
Cleanup and First Boot
Once you have the image on the SDCard, you should be able to put the card into your RaspberryPi and plug it in. If everything worked correctly, it should boot to the Operating System. Depending on the edition you have installed, this could be a simple TTY login or a graphical desktop environment.
Resizing the partitions
By default, the partitions that are created within the image are just large enough to support the OS. To have any usable space, you must first resize the partitions to fill the remainder of the sdcard. There is an included script that automates to minimize the risk of errors or data corruption. To run this script, simple run:
$ sudo resize-sd
Once completed, the script will prompt you to reboot the device. Once the reboot has finished, you should see that the available space has been completely filled with the root '/' partition and the filesystem has been resized to match.