tangent space at some point of a quasi-projective variety

Question

In order to define the tangent space to a quasi-projective variety $V$ (i.e a locally closed closed subset of $\mathbb{P}^n$ considered with Zariski topology induced from $\mathbb{P}^n$) at a point $p$ we must think of $V$ as an open subset in a closed sub variety $W$ of some fixed projective space. Could any one explain me with a simple example that how the tangent space is at some point of a Quasi Proj.Variety?