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$$9.8\ \mathrm{m/s}$)
- The value of $R_e$$R_\mathrm e$, the radius of the Earth (approximately $6378.1 km$$6378.1\ \mathrm{km}$)
- The value of $G$, the gravitational constant (approximately $6.67×10^{-11} N m^2/kg^2$$6.67\times10^{-11}\ \mathrm{N\ m^2/kg^2}$)
and solving the following equation:
$mg = \frac{GM_em}{R_e^2}$$$mg = \frac{GM_\mathrm em}{R_\mathrm e^2}$$ or $M_e = \frac{g R_e^2}{G}$$$M_\mathrm e = \frac{g R_\mathrm e^2}{G}$$
Now:
- to measure $g$ you can use a pendulum -– this can be done at home.
- to measure $R_e$$R_\mathrm e$ the simplest experiment is Eratosthenes' experiment -– this cannot be done at home
- to measure $G$ you need to use a Cavendish balance -– 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.).