You might wanna start at a slight angle to start the boinging.
The reason why the boinging makes it move back and forth: (images taken from sector_y)
Start from the bottom mount, then swing it to a vertical mount.
http://sector_y.yoyoing.com/Tricks/String_Tricks/Boing-E-Boing/boing-8.gif
Using that momentum, let the yoyo go forward, without moving your throwhand forward, just lower it down to go closer to your freehand.
http://sector_y.yoyoing.com/Tricks/String_Tricks/Boing-E-Boing/boing-9.gif
Then, it will look like this when the momentum brings it forward.
http://sector_y.yoyoing.com/Tricks/String_Tricks/Boing-E-Boing/boing-10.gif
Then, you take your throwhand up, this will put the strings together, and make the yoyo come back to the position it was at first.
http://sector_y.yoyoing.com/Tricks/String_Tricks/Boing-E-Boing/boing-11.gif
Then, you let the momentum carry it back, by lowering your throwhand again.
http://sector_y.yoyoing.com/Tricks/String_Tricks/Boing-E-Boing/boing-12.gif
Do it fast.
All pictures from sector y, i did not make them.