You accept a double made by your opponent by clicking on the offered double cube at the board. If you want to decline the double, you can right click on the cube.
There are also three buttons in the toolbar for handling cube offers. These buttons are marked Accept, Decline and Beaver. The beaver button is only activated in money game sessions where beavers are allowed.
The toolbar double buttons.
There are also menu options from the drop down menu for all the cube actions. Click Game->Take from the menu, to accept an offered double(<Ctrl><T>). Click Game->Drop, from the menu, to to decline an offered double(<Ctrl><P>). Click Game->Beaver, from the menu, to beaver an offered double.