Let $X$ be a smooth projective variety over $\mathbb{C}$.
And let $L$ be a big and nef line bundle on $X$.
I want to prove $L$ is semi-ample($L^m$ is basepoint-free for some $m > 0$).

The only way I know is using Kawamata basepoint-free theorem:

Theorem. Let $(X, \Delta)$ be a proper klt pair with $\Delta$ effective. 
Let $D$ be a nef Cartier divisor such that $aD-K_X-\Delta$ is nef and big for some
$a > 0$. Then $|bD|$ has no basepoints for all $b >> 0$.

**Question. What other kinds of techniques to prove semi-ampleness or basepoint-freeness 
of given line bundle?**

Maybe I miss some obvious method. Please don't hesitate adding answer although you think your idea on the top of your head is too elementary.