"Arrumar a mesa" is also very common, "Preparar a mesa" is also used.
"To put the table in the kitchen" -> "Colocar a mesa na cozinha" or "Levar a mesa para a cozinha".
Note the context, "Colocar a mesa" could mean both to put the table somewhere or to set the table.
I saw the possible correct answers that DL gives and one was "fixe the table" It might be somewhat correct for some English people to say "fix" the table, but it used less in my part of the world. I think I have heard people say this, but "fixe" is not even in the dictionary for English.
Here we have another instance in which one of the answers that DL says is an acceptable translation is not accepted. I put "I am going to place the table" (and "place" is given as an acceptable translation), meaning "put" the table -- as in move it somewhere and place it in a certain spot. Not sure why this would not also be acceptable. As to "laying" the table, American English speakers would never use "lay" to "set" a table before eating a meal. "Laying" a table would make no sense to us and we would think it had something to do with folding the legs and laying the table down on the floor, or up against a wall for storage -- as in a folding table.