What is the personal a in Spanish?

It is the preposition a placed before a direct object when that object is a specific person or animal: busco a mi hermano (I'm looking for my brother). It has no English translation - it is a grammatical marker, not the a that means 'to'. Compare busco a mi hermano (a specific person) with busco un piso (a thing, no a). The marker tells the listener the object is human and definite.

Do you use the personal a after tener?

Usually no. Tener normally drops the personal a even with people: tengo dos hermanos (I have two brothers), not tengo a dos hermanos. The exception is when tener means to hold or to keep someone somewhere, or when the relationship is emphasised: tengo a mi madre en el hospital (I have my mother in hospital). As a rule of thumb, plain possession after tener takes no a.

Does the personal a appear before alguien and nadie?

Yes. The indefinite pronouns alguien, nadie, alguno and ninguno refer to people, so they take the personal a as direct objects: no veo a nadie (I can't see anyone), busco a alguien (I'm looking for someone). This holds even though the person is not named or specific - what matters is that the referent is human.

The Personal A

Spanish puts the preposition a in front of certain direct objects. It looks like the a that means "to", but it is not - it carries no translation. Its only job is to mark that the direct object is a specific person (or an animal or thing the speaker treats like one). English has nothing equivalent, which is exactly why learners forget it.

The contrast in one line:

Veo a María. (I see María.) - a specific person, so a.
Veo la casa. (I see the house.) - a thing, so no a.

The core rule

Use the personal a when the direct object is a specific human being. That is the whole rule. Everything else is a refinement of "specific" and "human".

Busco a mi hermano. (I'm looking for my brother.)
Conozco a tu jefe. (I know your boss.)
Llamo a Laura. (I'm calling Laura.)
¿Has visto a los niños? (Have you seen the children?)

Compare those with their thing-objects, which take no a:

Busco un piso. (I'm looking for a flat.)
Conozco esa calle. (I know that street.)
Llamo un taxi. (I'm calling a taxi.)

When it applies

Named or specific people. Any human direct object you could point at: a friend, a relative, a named person, a defined group.

Vi a Carlos en el centro. (I saw Carlos in the centre.)

Pets and personified animals. A loved animal gets the same treatment as a person. A generic, unspecified animal does not.

Quiero mucho a mi perro. (I love my dog very much.) - the family pet, so a.
Quiero comprar un perro. (I want to buy a dog.) - any dog, no a.

Indefinite persons: alguien, nadie, alguno, ninguno, quien. These pronouns refer to people, so they trigger the a even though no specific person is named.

No veo a nadie. (I can't see anyone.)
Busco a alguien que hable francés. (I'm looking for someone who speaks French.)

Personified things. Countries, organisations and abstractions that are treated as people in elevated or emotional speech can take the a: temían a la muerte (they feared death).

When it does not apply

After tener (plain possession). This is the big exception. Tener normally drops the personal a even with people.

Tengo dos hermanos. (I have two brothers.) - no a.
Tiene una hija. (She has a daughter.) - no a.

The a comes back when tener means "to hold/keep someone" rather than "to possess": tengo a mi madre en casa (I have my mother staying at home).

Non-specific or hypothetical people. When the person is an unknown, not-yet-identified "any such person", the a is dropped (often with a subjunctive verb).

Necesito un médico. (I need a doctor.) - any doctor, no a.
Busco una persona que sepa cocinar. (I'm looking for a person who can cook.) - no specific person in mind.

Things, places and ideas. Non-human direct objects never take the personal a: veo la casa, compro el coche, estudio la historia.

A quick reference

Situation	Personal a?	Example
Specific named person	Yes	Veo a María.
Specific group of people	Yes	Llamo a los niños.
A loved pet	Yes	Quiero a mi gato.
alguien / nadie / alguno	Yes	No conozco a nadie.
Thing, place or idea	No	Veo la casa.
Plain possession with tener	No	Tengo dos hermanos.
Non-specific / hypothetical person	No	Busco un médico.
Generic, unspecified animal	No	Quiero comprar un perro.

Common mistakes English speakers make

Dropping it before named people. The instinct from English is to say veo María. It must be veo a María. This is the single most common slip, because English gives you no reason to expect the marker.

Adding it after tener. Over-correction the other way: learners who have learned the rule then say tengo a dos hermanos. Plain possession takes no a.

Forgetting it with nadie and alguien. No veo nadie is wrong; it is no veo a nadie. The referent is human, so the marker is required even though no individual is named.

Confusing it with the directional a. The personal a ("veo a Laura") and the a of motion ("voy a Madrid") look identical but do different jobs. Do not assume an a before a noun always means "to".