Look for the verb (the action word) in the sentence. For instance, in the sentence "Mary drove to work," the word "drove" is the verb.
Ask yourself who or what is doing the action of the verb. In the sentence "John arrived first at work," the verb is "arrived." By asking yourself who arrived, you can establish that "John" is the subject.
Look for the connecting word "and," which can be used to connect multiple subjects. In the sentence "John and Mary finished their work," both "John" and "Mary" are subjects.