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 $9.8\ \mathrm{m/s}$)
 - The value of $R_\mathrm e$, the radius of the Earth (approximately $6378.1\ \mathrm{km}$)
 - The value of $G$, the gravitational constant (approximately $6.67\times10^{-11}\ \mathrm{N\ m^2/kg^2}$)

and solving the following equation:

$$mg = \frac{GM_\mathrm em}{R_\mathrm e^2}$$ or $$M_\mathrm e = \frac{g R_\mathrm e^2}{G}$$

Now: 

 - to measure $g$ you can [use a pendulum][1] – this **can** be done at home.
 - to measure $R_\mathrm e$ 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