Please help me how to do click button to display select box.
at the same time add and remove select box

Are you using jquery or pure javascript?

please help me add and remove select box get values from database

Please show code you have so far. It is hard to guess without seeing it.

In general in jquery you use show and hide methods. The elements have to have classes or ids so you can target them with jquery.

What functionalities would you like ajax to carry out? As said, hard to help without code.