Conjugated tenses:

root +	Preterite		Imperfect
	-ar	-er, -ir	-ar	-er, -ir
yo	-é	-í	-aba	-ía
tú	-aste	-iste	-abas	-ías
usted, él/ella	-ó	-ió	-aba	-ía
nosotros/as	-amos	-imos	-ábamos	-íamos
vosotros/as	-asteis	-isteis	-abais	-íais
ustedes, ellos/ellas	-aron	-ieron	-aban	-ían

preterite, simple past (pretérito indefinido, pasado simple):

• refers to a single action (event) that took place in the past and was completed in the past or for a specific time
  e.g., Llamé a las once – I called at 11.
  Te llamé dos veces – I called you twice.
  Él vivió allí por cinco años – He lived there for 5 years.

imperfect (pretérito imperfecto):

• refers to any repeated, continuous/usual, background, or habitual past action (“used to...”), also time/ages in the past, also description (people, places)
  e.g., Usualmente él llegaba temprano – He usually arrived early.
  La ciudad era vieja y sucia – The city was old and dirty.
  Isabel tenía ocho años – Isabel was eight years old.

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Compound tenses:

perfect, present perfect (preterito perfecto):

haber + past participle   {he, has, ha, hemos, habéis, han} + root{ado, ido}

• refers to an action that began in the past and has completed in the present (or continues or affects the present)
  e.g., He comido gambas – I have eaten prawns
  Juan ha pagado las cuentas – Juan has paid the bills
  He perdido los libros de español. ¿Los tiene aquí? – I have lost the Spanish books. Do you have them here?
  Juan y María han viajado a España – Juan and Maria have traveled to Spain
  ¿Qué ha pasado? – What’s happened?
  ¿Has ido a Francia? – Have you been to France? ... muchas veces ...
  José se ha levantado tarde – José got up late (reflexive)
  Me he duchado – I showered (myself, reflexive)

past perfect, pluperfect (pluscuamperfecto):

haber imperfect + past participle   {había, habías, había, habíamos, habíais, habían} + root{ado, ido}

• refers to an action that began in the past and has completed to some related time in the past (or affected that time)
  e.g., Había caminado a la tienda – I had walked to the shop

  Yo siempre había querido ser ingeniero – I had always wanted to be an engineer

past anterior, preterite perfect

haber preterite + past participle   {hube, hubiste, hubo, hubimos, hubisteis, hubieron} + root{ado, ido}

• used (literary/written) to express an action that ended immediately before another past action

  Miguel hubo estado en la casa ... – Miguel had been in the house when ...

past perfect progressive:

estar past + gerundio

• tells what a person was doing and completed
  e.g., Estuve leyendo desde las cinco hasta las seis – I was reading from five until six

past imperfect progressive:

estar imperfect + gerundio

• similar to the imperfect; tells what a person was doing (e.g., when interrupted)
  e.g., Estaba caminando a la tienda cuando encontré un billete de veinte euros – I was walking to the shop when I found a twenty-euro note.

immediate past:

acabar present + de + infinitive – to have just [English past participle]

• completed in the very recent past
  e.g., Acabo de caminar a la tienda – I just walked to the shop (lit: I finish at to walk to the shop)

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Using the past/imperfect tense of ir + a + infinitive can be useful, too:

Fui a comer paella – I went to eat paella

Iba a comer paella – I was going to eat paella

Iban a escuchar la radio – they were going to listen to the radio

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English background:

‘preterite’ (adj, n) – expressing a past action or state, simple past tense or form <L praeter (past, beyond) + ire (go)

‘pr[a]eter-’ (prefix) – past, beyond <L; e.g., ‘preternatural’