How can I go about obtaining the activation enthalpy of a reaction using the Arrhenius Equation experimentally? I plan to do a string of experiments on the kinetics of the decomposition of hydrogen peroxide. I’m going to see the effect of catalyst concentration on rate and the effect of varying hydrogen peroxide concentration on rate, which will then allow me to formulate a rate equation for the reaction. 

I would also like to calculate the activation enthalpy of the reaction specifically using the Arrhenius Equation $k=A\operatorname{e}^\tfrac{-E_\mathrm{a}}{RT}$. How would I do this? As far as I’m aware I should use varying temperatures in the reaction to get different values of the rate, but I’m not sure.

So what kind of experiment should I do (varying temperature to see the change in rate?)?

What should I do with my results?

Is the value of $E_\mathrm{a}$ obtained from analysing a specific graph that will be drawn up, and if so what graph would this be?
Experiments at various temperatures will allow you to calculate $E_a$. This is clear from a putting the Arrhenius equation in a different form:

$$\ln{k}=\ln{A} + \frac{-E_a}{RT}$$

A plot (or linear regression) of $\ln{k}$ vs $\frac{1}{T}$ yields $\frac{-E_a}{R}$ as the slope. The same experiment with a catalyst will show the activation energy is decreased.