You use Object Snapping for this: Place the cursor near the desired point and press the middle mouse button (unless you have the middle button set up as double click in which case this won't work ... you can press 'n' on the keyboard as an alternative to the middle button).
The behaviour of Object Snapping can be set in the Object Snap Menu (S3 on the Utility Menu). From this menu you can set the Miss Distance (s4 : how close you need to be to the point to snap to it), and the types of things you want to snap to (you will need F2 End-Point enabled to snap to the end of existing lines, but there are quite a few other options as well ... end point should be enabled by default unless you have changed it)