In Hartshorne's book Algebraic Geometry he says in Example 3.3.5 in Chapter IV (p. 309):
If $X$ is a plane curve of degree 4, then $D=X.H$ is a very ample divisor of degree 4.
Here $H$ is a hyperplane section for a projective embedding. Why is this divisor very ample?
It is very ample by definition: If $i:X \to \mathbb{P}^2$ is the projective embedding then $\mathcal{L}(D) = i^*\mathcal{O}_{\mathbb{P}^2}(1) = i^*\mathcal{O}_{\mathbb{P}^2}(H)$ is a very ample line bundle by (Hartshorne, p.120 Definition). By Hartshorne p.307 a divisor $D$ is called very ample if $\mathcal{L}(D)$ is very ample.