What are significant figures?
They are the digits that 'count' or 'matter'
Consider for example if a microscope can measure with an accuracy of a hundredth and it measures that small object is 0.25 units. Well, that means that if we use this microscope's measurements in some other calculations then we never really can be more accurate than the hundredth place.
314  3 significant digits 
310  3 significant digits 
0314  3 signficant digits 
304  3 significant digits 
001  1 significant digit 
200  2 significant digits 
200  2 significant digits 
 leading zeros do not count (see examples 3 and 5)
 If you have several trailing zeros like examples 6 and 7, then you can underline the last significant digit (example 7) OR you can overline it like example 6.
Significant Digits Less than 1, like .0015
You do not count the leading zero's.
So, there are 2 significant digits in .0015
Practice Problems
Number  How many significant figures? 

0.12 
Two

0.012 
Two

0.00120 
4 
300.0 
4 
300 
2 
300 
1 