How to use polar coordinates in a problem with the heat equation?

Question

I have the problem:
Use the separation variables method to solve the following problem about heat conduction in a infinity circular cylinder. $$\begin{cases} u_t-\Delta u=0, & B_1(0)\times (0,\infty) \\ u=0, & \partial B_1(0)\times (0,\infty)\\ u(x,0)=f(|x|), & x\in B_1(0) \end{cases}$$ where $B_1(0)\subset\mathbb{R}^3$. The suggestion is that I have to use polar coordinates and as the initial data its independent of $\theta$, then search solutions independents of $\theta$.
I don´t know how to start or where I can find information to solve this.
Please, I am really bad to differential equations.