[wrholt]

Any noun that functions as an indirect object (objeto indirecto = OI) is introduced with the preposition "a". It doesn't matter whether the noun identifies a person or not, and it doesn't matter whether the noun is definite and specific or not.

On the other hand, a noun that functions as a direct object (object directo = OD) may or may not be introduced by the preposition "a".

When a direct object refers to a specific person or animate being that is viewed as a person, one normally introduces that direct object with the preposition "a". (This use of the preposition "a" is commonly called "personal a".) For example:

"Busco a una secretaria que habla español" = "I'm looking for a secretary who/that speaks Spanish".

Using the preposition "a" to introduce the direct object "una secretaria" in combination with using the indicative mood in the relative clause unambiguously indicates that the secretary in question is a particular woman known to the subject who is a secretary and who can be identified by the fact that she speaks Spanish. In this case the direct object refers to a specific person.

On the other hand, when a direct object does not refer to a specific specific person or animate being, normally one does not use the preposition "a" to introduce the direct object. For example:

"Busco una secretaria que hable español." = "I'm looking for a secretary who/that speaks Spanish".

Not using the preposition "a" to introduce the direct object "una secretaria" in combination with using the subjunctive mood in the relative clause unambiguous indicates that the speaker does not know whether or not such a person exists.

Another example:

"Busco la pluma de mi amiga" = I'm looking for my friend's pen.

The direct object is the inanimate noun "la pluma". This is a specific direct object, but it's not viewed as a "person" in any sense, and one does not introduce this direct object with the preposition "a".

There are occasions when one may or must use the preposition "a" to introduce a direct object that is non-living. This typically occurs when both the subject and the direct object are non-living things and it would not otherwise be clear which one is the subject and which one is the direct object; the one introduced by the preposition "a" is the direct object, and the other one is the subject.