First you often need to find the shape. Exactly how depends on what
data you are given. You need five data to define a quadrilateral:
for example, neither four angles nor four edges is enough.

Usually next you divide it into triangles and using trig

triangle area = a x b x sin(C)/2

where a,b are the lengths of two edges, C the angle between them.

or vector cross product

triangle area = 1/2 (X-Y) x (Z-Y).

*If you know it's a rectangle (or any parallelogram) use the formula Area = Base x Height. If you know it's a trapezoid, the area is the average of the parallel edges times the distance between them.

*If you are given integer coordinates and you can sketch it accurately on a grid you can count cells, or use Pick's Theorem, which says that the area of any grid polygon is

# of grid points inside
+ 1/2 # of grid points on boundary
- 1

Good Hunting!
-RD