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The P agrees with the S in person and number. But in Modern English there's often a conflict between form and meaning. Agreement of the P with the S is restricted to the present tense apart from the verb "to be", because it agrees with the S not only in the present but also in the past.

PLURAL:
• Two or more homogeneous subjects connected by the conjunction "and" or asyndetically (Her father and mother were completely out of breath);
• A subject expressed by a noun modified by two or more attributes connected by "and" when two or more persons, things or ideas are meant (Heavy and light music have their own admirers);
• The subject expressed by a collective noun denoting the individuals of the group taken separately (people, infantry, cavalry, gentry, clergy, police, cattle, poultry, jury, etc.) (Hurry up, the police are coming!)
SINGULAR:
• Two or more homogeneous objects expressed by infinitives (To live and to find peace was all he needed);
• The sentence beginning with "here" or "there" (In the room there was a small chair and a big table);
• Two homogeneous subjects in the singular connected by the conjunctions "not only… but", "neither… nor", "either… or", "or", "nor" (Not only the rain stopped, but the wind also was gone);
• Two subjects in the singular connected by the conjunction "as well as" (The album "In Rock" as well as "Machine Head" has contributed a lot into the development of heavy rock);
• A subject expressed by a noun modified by two or more attributes connected by "and" when one person, thing or idea is meant (The big, bad and blood-red moon was looking down at the Earth);
• The subject expressed by a defining, indefinite, or negative pronoun (Everybody is going to get good marks; There was something pleasant in her words; Nobody leaves the room until I say so);
• The subject expressed by the emphatic "it" (Many agree that it is English businessmen who can be trusted);
• The title of a book, the name of a newspaper or magazine (even if the noun is in the plural) ("Great Expectations" was written by Dickens);
• The subject denoting time, measure, or distance when the noun represents the amount or mass as a whole (Five dollars is not a big sum when we talk about this item);
• The subject is expressed by a collective noun denoting a group or collection of similar individuals taken as a whole (mankind, humanity, etc.) (If the mankind is going to see the end of this century, it is bound to survive);
• The word-group "many a…" (Many a politician is a liar);
• Arithmetic calculation (addition, subtraction, division; multiplication is an exception – it can be both) (Six and four is ten; Thrice two is (are) six);

Some more information about English grammar.