  We develop a technique for gluing relative trisection diagrams of
$4$-manifolds with nonempty connected boundary to obtain trisection diagrams
for closed $4$-manifolds. As an application, we describe a trisection of any
closed $4$-manifold which admits a Lefschetz fibration over $S^2$ equipped with
a section of square $-1$, by an explicit diagram determined by the vanishing
cycles of the Lefschetz fibration. In particular, we obtain a trisection
diagram for some simply connected minimal complex surface of general type. As a
consequence, we obtain explicit trisection diagrams for a pair of closed
$4$-manifolds which are homeomorphic but not diffeomorphic. Moreover, we
describe a trisection for any oriented $S^2$-bundle over any closed surface and
in particular we draw the corresponding diagrams for $T^2 \times S^2$ and $T^2
\tilde{\times} S^2$ using our gluing technique. Furthermore, we provide an
alternate proof of a recent result of Gay and Kirby which says that every
closed $4$-manifold admits a trisection. The key feature of our proof is that
Cerf theory takes a back seat to contact geometry.
