Why my wall sockets are buzzing when I plug something in?
The socket spring is sprung.  The buzzing says you have arcing in there.  Very bad news.  I suspect the wire is getting loose because it's a type of connection we call a "back stab" where you jab the wire in a hole and a barbed spring grabs it, I bet that has also sprung. I would shut off the breaker and swap the outlets for quality grades. 

How do you learn how to do that?  Libraries and big-box home improvement shops have a collection of books that teach home electical repairs.   Look through all of them and find one that "speaks to you".  

When you shop for outlets, you'll find there's a 75 cent tier, a $3-4 tier and a $10-12 tier.  You want the $3-4 tier.

Never use the "back stabs" on the outlet where you jab the wire in, and it grabs it.  The springs are unreliable - this very thing happens.  It is OK to use "clamp-screw" types where you stick the wire into a slot and then screw down the screw to clamp it down.  Those are in the $3-4 tier.   Or use the screw terminals. 

Also be on the lookout for "aluminum wire" - it is silver or gray instead of orangish copper.  Aluminum wire requires very special handling - check back here.