덮다(deop-da, deopda)
To place something over another object to cover or block it
When to use
Covering food with cloth, Covering book with paper, Snow covering mountains
The nuance
덮다 is mainly used when covering a flat or wide surface by placing a cover, cloth, paper, etc. on top.
씌우다(ssui-u-da, ssuiuda)
To put a cover or clothing snugly onto an object
When to use
Putting a cover on a car, Putting a hat on the head, Putting glasses on
The nuance
씌우다 is used when fitting a cover, hat, glasses, etc. snugly onto an object, implying it is fixed or secured in place.