You can't measure the mass of Earth directly, as others have stated. You can calculate it knowing:

 - The value of $g$, the gravitational acceleration (approximately $9.8 m/s$)
 - The value of $R_e$, the radius of the Earth (approximately $6378.1 km$)
 - The value of $G$, the gravitational constant (approximately $6.67×10^{-11} N m^2/kg^2$)

and solving the following equation:

$mg = \frac{GM_em}{R_e^2}$ or $M_e = \frac{g R_e^2}{G}$

Now: 

 - to measure $g$ you can [use a pendulum][1] - this **can** be done at home.
 - to measure $R_e$ the simplest experiment is [Eratosthenes' experiment][2] - this **cannot** be done at home
 - to measure $G$ you need to use a [Cavendish balance][3] - which cannot be done at home because it's a notoriously difficult experiment (the constant is really small, requires custom apparatus, a very long time, etc.).


  [1]: http://en.wikipedia.org/wiki/Pendulum#Gravity_measurement
  [2]: http://en.wikipedia.org/wiki/Eratosthenes#Eratosthenes.27_measurement_of_the_earth.27s_circumference
  [3]: http://en.wikipedia.org/wiki/Cavendish_experiment