Let's look, briefly, at the related concept of the gravitational field. The way you know that there is a gravitational field is if you drop something and it falls (this is assuming that you are not in an accelerating frame of reference). We can define the gravitational field as the force that a mass would "feel", divided by the mass itself.
Similarly, the way you would know if there is an electric field is to release a charged particle and see if it starts accelerating. Of course, you would need to know that it isn't accelerating due to some other force, like gravity. Let's assume that you know how gravity would affect the charged particle, and the particle accelerates in a way different from that. Then you could attribute the different acceleration to an electric field. The electric field is defined as the electric force that a charge would "feel", divided by the charge itself.
The measurement consists of releasing the mass or charge and seeing what force it experiences.