In order to measure distance in your own frame you get a ruler.  However, you can't measure moving things the same way.  If you try to measure a train by running along side it with a ruler, then you're no longer in your own frame.
To measure a moving object you get a stopwatch and time how long it takes for the object to pass.

One of the weird effects of relativity is that fast objects shrink in the direction of their movement.
Here's why:

In the train analogy it can be seen that time is "skewed", seen from inside the train events at the front are seen as happening earlier (as compared to how a someone watching the train pass would claim), and events at the back are later.
Cross your eyes and try to picture the situation from the point of view of someone outside the train, watching it pass.  They will see the front of the train arrive late (on time onboard, since they see things sooner), and the back of the train arrive early (right on time in the train again).
But, if the front of the train is early and the back is late, then the train will literally shrink.  Seriously.



Technically...
As always, phrase the question in the form of two events.
Since the yardstick is moving in order to measure it you can stay put and time how long it takes for the stick to pass.  So event one is the front of the stick passing you, and event two is the back of the stick passing.


In your frame the two events happen in the same place, so X = 0.  The length of the stick is L = VT.
So:



This here is the reference frame of the stick.  It sees you and your stopwatch move from the front to the back at speed V.  Given that the yardstick is L' in length at rest:


The interval between the events must stay the same.

So the length as measured from a moving observer is shorter, by a factor of .