Hi, I'm a newbie to cycling and wondering what's the proper way to shift gears to prevent the chain from rattling?

Endeavour to keep the chain as straight as possible. This means if you're on a large gear in front, it should be on a small at the back and vice versa.

https://www.sheldonbrown.com/gears.html

Also perform a search on this forum - this topic has been covered many times and you'll find some good information!

Are you talking about a bike with index shifting, or friction? Can you describe the rattling?

Chain noise can be a grinding sort of noise that happens when friction shifting is trying to move the chain to a larger chainwheel or rear sprocket. It can also be something continuous after you shift, coming either from the front or the back. This latter noise results from the front cage not being centered on the chain and rubbing the chain. In the rear it results in the rear cage not being positioned to feed the chain directly onto the sprocket. It can also be caused by chain or rear sprocket wear that causes the chain to hang up momentarily on the little hooks that you can see on a badly worn sprocket. This problem requires replacement of the whole freewheel or cassette and the chain, at the same time, and it happens on friction and on indexing systems.