RouterBoards can netboot OpenWrt initramfs .elf (.bin in some instances) images via TFTP. This RAM-based initramfs OpenWrt image is first used to validate the desired OpenWrt version operates properly without overwriting any existing image in the NAND or NOR flash of the RouterBoard.

Once you have verified OpenWrt is working on your MikroTik hardware, use the LuCI web interface to permanently flash the appropriate sysupgrade .bin image into the flash of the RouterBoard. In this way, an initial installation is treated exactly the same as a subsequent OpenWrt upgrade. Prior versions of OpenWrt required a subsequent upgrade to once again boot OpenWrt using initramfs: with the current version of OpenWrt that now uses Unsorted Block images (UBI), the initial flash and subsequent upgrades can be performed directly in-place from the LuCI web interface.

After OpenWrt is installed to Flash, depending on the model, some platform configuration may be needed. This is explained in the model specific wiki pages.
First Things First: Don't Lose Your RouterOS License

Before you start installing OpenWrt, save your RouterOS License .key file. This will allow you to use Mikrotik's NetInstall to re-install RouterOS.
Save your license by using Mikrotik WinBox: it's under System→License→Export Key. The Mikrotik WebFig web interface does not export license files, you must use WinBox.

See below for other methods to export your license file.