El Verbo "Haber"

You may think it strange to devote an entire page to a single verb, but haber is a very major Spanish verb used as practically the only helping verb in the entire language. We'll map out its entire conjugation table below:
  Yo Él/Ella/Usted Nosotros Vosotros Ellos/Ustedes
Present he has ha / hay hemos habéis han
Preterit hube hubiste hubo hubimos hubisteis hubieron
Imperfect había habías había habíamos habíais habían
Future habré habrás habrá habremos habréis habrán
Conditional habría habrías habría habríamos habríais habrían
Subjunctive haya hayas haya hayamos hayáis hayan
hubiera hubieras hubiera hubiéramos hubierais hubieran
hubiere hubieres hubiere hubiéremos hubiereis hubieren
Gerund habiendo
Participle habido
You may be wondering what the bolded words are for and why there are two words for the 3rd person singular present indicative conjugation, but to answer those questions, we must tell you that haber functions as two separate verbs: the first is as a verb that can be most easily defined as "to be (there)" as in "to exist"; and the second is a helping verb used to make participles. We'll explain them in that order:

HABER - to exist

In Spanish I, students learn to say "there is" or "there are" by using the word hay, which is an alteration of the 3rd person singular present indicative conjugation of haber. By using the 3rd person singulars of haber, you indicate existence:

Hay cuatrocientos personas en el estadio - There are four hundred people in the stadium

Note how - even though the subject is plural - the verb does not differentiate between singular and plural. You can change the tense simply by using a different tense of haber:

Mañana no habrá ningunos asientos en este salón - Tomorrow there will be no seats in this room

The words in the table above that are bolded are those that are used in this sense of haber. Note that hay is a special form of haber that is only used here!!

HABER - the helping verb "to have"

In English, we often use the helping verbs "have, had, will have had, etc."; Spanish does the same, and - like with English - these are designated by a verb. However, where English simply uses "to have", Spanish has its own verb. Haber forms the helping verb, but - like in English - this must be followed by a participle. But how do you make a participle in Spanish? It's similar to the gerund, and even simpler:
AR -ado
Therefore, "I will have spoken" is "Habré hablado". Note how, like the progressive, you conjugate the helping verb and simply add the participle. However, also like the progressive, there are irregular participles!:
hacer hecho
rehacer rehecho
deshacer deshecho
poner puesto
exponer expuesto
oponer opuesto
disponer dispuesto
morir muerto
romper roto
decir dicho
pudrir podrido
abrir abierto
cubrir cubierto
encubrir encubierto
volver vuelto
revolver revuelto
devolver devuelto
envolver envuelto
escribir escrito
ver visto
freír frito
Here are a few examples:

Me hube revuelto cuando él me atacó - I had turned around when he attacked me
El general ya ha expuesto el plan a los soldados - The general has already laid out the plan to the soldiers
Habrá salido en el momento en que lo lleguemos - He'll have left by the time we reach him

Note that you can also use haber in infinitive form:

Habré tenido que haberlo hecho - I will have had to have done it

Finally, haber de... is a phrase meaning "to have to (do something)" (just like tener que...):

Habré habido de haberlo hecho - I will have had to have done it

However, this phrase is usually used in the infinitive to avoid confusion:

Haber de hacer la tarea es muy molesto - Having to do homework is very annoying

Also, this phrase is typically formal:

Dios decide lo que ha de ser - God decides what is to be

It needs to be mentioned that haber always directly precedes it participle, even before objective/reflexive pronouns. The following sentence shows the correct order of all of them together:

Se le lo ha dado - One has given it to him

(reflexive) + (indirect) + (direct) + (helping verb) + (participle)