Creating a translation in Geogebra requires a little planning ahead. You need to create the vector that you want to use for translation first. Choose the vector tool from the toolbar and draw the vector that you want to translate by. The vector can be drawn anywhere on the plane, it doesn't have to start at A. Then click on the Translate by Vector tool, click point A, then click the vector you created.

You can now go back and change some of your original information. You can change the original location of point A, or you can change the length/direction of the vector. The drawing will update so that A' is always the translation of A by the vector.