Los verbos modales (can, must, should, may, might, will, would...) matizan el verbo principal: expresan capacidad, obligación, permiso, consejo o probabilidad. Tienen dos rasgos que el hispanohablante debe grabarse: nunca cambian de forma (no llevan "-s" en tercera persona: she can, no "she cans") y el verbo que les sigue va en infinitivo sin "to" (you must go, no "to go"). Elegir el modal correcto es elegir cuánta fuerza o certeza le das a la frase.
La regla de oro
Sin "-s" ni "to" tras un modal: she must go, he can swim.
Qué hace cada uno
ENcan/could = ability/permission · must = strong obligation · should = advice.
EScan/could = capacidad/permiso · must = obligación fuerte · should = consejo.
ENmay/might = possibility · will = certainty/future · would = conditional/preference.
ESmay/might = posibilidad · will = certeza/futuro · would = condicional/preferencia.
ENought to = should (advice, a touch more formal): You ought to apologise.
ESought to = should (consejo, algo más formal): You ought to apologise.
Must vs have to
ENmust = the speaker's own obligation, can't change tense. have to = external rule, flexible (had to, will have to).
ESmust = obligación propia del hablante, no cambia de tiempo. have to = norma externa, flexible (had to, will have to).
ENBeware: mustn't = forbidden, but don't have to = not necessary — opposite meanings.
ESOjo: mustn't = prohibido, pero don't have to = no hace falta — sentidos opuestos.
El error típico del hispanohablante
Sin "to": I can help, no "I can to help".
mustn't ≠ don't have to: you mustn't smoke (prohibido) vs you don't have to come (opcional).