더하다 means "to add or increase. " 더하다 is used for the general meaning of "to add". 추가하다 means "to put in more of something later. " 추가하다 is used when someone add something LATER. 덧붙이다 means "to make an addition to something that already exists or that one has been working on. " 덧붙이다 is used when someone attach patches to something or add comments to talks or documents.