How to parameterize a manifold?

Question

If I have $M$ be a set in $\mathbb{R}^3$ defined by $x-y^2+z^2=0$ and $y^2+z^2<4$, how would I find a function from $\mathbb{R}^d \rightarrow \mathbb{R}^3$ ($d$ is the dimension of the manifold)that parameterizes $M$?