- I saw the tree.
- I saw Teresa.
- Vi el árbol.
- Vi a Teresa.
The basic rule is a simple one: the a precedes the mention of a specific person or persons used as a direct object, and (except in some rare cases where it's used for clarification) it is not used in other cases. Levantó la taza, he lifted the cup. Levantó a la muchacha , he lifted the girl. Oigo la orquesta, I hear the orchestra. Oigo a los músicos, I hear the musicians. Recuerdo el libro, I remember the book. Recuerdo a mi abuela, I remember my grandmother. The a is not used if the object doesn't refer to anyone specific. Conozco a dos carpinteros, I know two carpenters. But, necesito dos carpinteros, I need two carpenters.
Although the basic rule is quite simple, there are a few exceptions (aren't there always?), and even an exception to an exception.
The exceptionsWith certain pronouns: This is really more of a clarification rather than an exception. When used as direct objects, the pronouns alguien (somebody), nadie (nobody) and quién (whom) require the personal a. So do alguno (some) and ninguno (none) when referring to people. No veo a nadie, I don't see anyone. Quiero golpear la pared, I want to hit the wall. Quiero golpear a alguien, I want to hit somebody. ¿A quién pertenece esta silla? Whose chair is this? ¿Taxis? No vi ningunos. Taxis? I didn't see any. ¿Taxistas? No vi a ningunos. Taxi drivers? I didn't see any.
Pets: Many pet owners think of their animals as people, and so does Spanish grammar, so the personal a is used. But the a isn't used with ordinary animals. Veo a mi perro, Ruff, I see my dog, Ruff. Veo tres elefantes, I see three elephants.
Personification: A country or object can be personified — treated as if it were a person. Use of the personal a often implies some sort of a personal relationship, such as an emotional attachment, with the noun personified. Yo extraño mucho a los Estados Unidos, I very much miss the United States. Abracé a la muñeca a causa de era mi amiga, I hugged the doll, for she was my friend.
With tener: Generally, the a is not used after tener. Tengo tres hijos y una hija, I have three sons and a daughter. No tengo jardinero, I don't have a gardener.
Exceptions to an exceptionAfter tener: The personal a is used after tener when it is used in the sense to hold someone or to have someone somewhere. Tengo a mi hijo en los brazos, I have my son in my arms. Tengo a mi hija en el pesebre, I have my daughter in the crib.
The personal a can also be used after tener when its usage suggests a particularly close or emotional relationship. Cuando estoy triste y necesito hablar, tengo a mis amigos, when I am sad and need to talk, I have my friends. But tengo amigos, I have friends.