What you Need
What to do
First extract the inner part of your biro.
Then saw the ends off so you have a tube that is the same diameter all the way along.
Clean up the cuts using a pair of nail scissors. (It may help if you make the edges slightly conical).
Now jam each end of the biro about 1cm into the potato; so you get a lump of potato stuck in each end.
Point one end somewhere safe, and push the lump of potato in the other end down the tube, using the rod.
What may happen
You should find that one of the lumps of potato fires off at an impressive speed.
Why does it happen?
The lumps of potato make a good airtight seal against the inside of the tube, because as they are jammed into the conical hole, they are compressed. This means that if you push one of the lumps along the tube, the gas between them is compressed, increasing its pressure.
The pressure increases until the force it exerts on the second lump of potato is high enough to overcome the friction that is holding it in the tube. As friction drops when something is moving (this is why it is often much harder to start pushing something than keep it going) there is now a very large pressure force on the potato, acting almost unopposed by friction, so the potato accelerates out of the tube very rapidly.
This is based on the the same principle as how toy spud guns work, but they use something more engineered to compress the air. Air guns also work in a similar way; pulling the trigger releases a large spring which pushes a piston down a cylinder. This compresses the air behind the bullet until it overcomes the friction holding it there, and then it fires down the barrel.
In fact, based on this same principle, there are designs for a gun used to fire projectiles into space. The prototype was called SHARP (Super High Altitude Research Project) and worked by using a methane-oxygen explosion to fire a piston down a tube. This then compressed hydrogen to enormous pressures, which forced the bullet/satellite up the barrel. Compared to current rocket technology, only a third of the rocket's weight would be taken up by the equipment used to project it, allowing it to get into low earth orbit far more efficiently than using present rocket technology.