Can you install a generic ROM on any device? I am relatively new to rooting and stuff. I have just rooted my android tablet. It's a Chinese tablet, not much about it is available on the internet.

Can I install ROM for another device on my tablet? I saw many videos on YouTube showing "How to install any ROM on any Android device". Does 'any' here mean that I can install, let's say, a Nexus ROM on my tablet?

Is there some generic ROM which can be installed on all androids? If so, can I install this generic ROM and then upgrade to a ROM of another device?

If no, is there a way to do so? (If not, then how do manufacturers put their ROM for the first time?)
You won't be able to install a ROM from a different device,  unless it is ported to your device - there are write-ups on the XDA forums on this. There isn't any generic ROM for all devices. Each device has its own chipset and hardware, that has its own firmware (software) design for it. In order for there to be a generic ROM, it would have to have the software and drivers for every device out on the market. The size of the ROM would be so large it wouldn't fit on most devices, let alone have room for anything else. Manufactures flash the ROM to their devices. From there we the can unlock the boot loaders, flash a custom recovery, install kernels and flash a custom ROM designed/made/ported for our device. 

Check out this link and search for your device. http://forum.xda-developers.com/. There are other forums on the internet, but you can search Google for them.