Haber loses its e before the future endings, exactly as poder does. It is a natural irregularity: imagine years of saying "habería" and hearing the vowel wear away.
haber + -ía → habría (I would have)
This unlocks a whole family of sentences: I would have gone, I would have been able to, and so on.
Habría ido · Habríamos comido · Habríamos podido ir · Habrían podido comer · Habrían venido a comer
Note the a in the last one: venir is a verb of motion, so it keeps its connecting a.
A framing worth adopting. Do not try to translate eaten, gone or been able, because those English forms are all wildly different. Just ask for the version of the verb that follows haber.
-ar → -ado · -er / -ir → -ido
ir → ido · poder → podido · gustar → gustado
Combine habría with gustar and you need the Spanglish step. I would have liked it is it would have pleased me.
That last one is they would have pleased us, so the verb goes plural while the nos stays put.
Should is simply would owe. Put deber into the -ía tense and you have it.
deber + -ía → debería (I should)
Deberías venir a mi casa · Deberías venir a mi casa a comer · Deberíamos hablar · Deberíamos hablarlo · Deberíamos hablarle · Deberíamos hablarles
Deberíamos hablarle could mean to him, to her, or to you formally. If you need to be clear, use the preposition instead.
Deberíamos hablar con ella
Sentences like we would have been able to go look complicated, and they take the same structure in both languages, so tackling each part individually keeps you in control.
habríamos · podido · ir
Daría · Darían · Me darían · Me lo darían