I know that an electric field is a region that surrounds a charged particle and exerts a force on the particle, but I don't know how to determine an electric field.
It depends on the problem being asked. Your textbook should have the equation for the electric field due to a point charge. Perhaps it also has equations for the electric fields of a line of charge as well as a charged plate or plane.
And sometimes, the electric field is simply a given in the problem statement.