Some verbs may, and some must, be followed by prepositional phrases. When they are, the prepositions are often fixed, although there are verbs that can go with more than one preposition. Here is a list of some prepositions and the verbs which usually precede them:
argue, boast, complain, decide, dream, hear, laugh, learn, lecture, preach, protest, quarrel, read, speak, think
Have you thought about my proposal at all?
They are protesting against the government.
aim, arrive, glance, guess, hint, laugh, look, marvel, shout, smile
They were very rude and laughed at him.
account, aim, allow, apply, apologize, arrange, ask, blame, care, call, cater, count, hope, long, pay, pray, provide, search, wish
How did they account for the missing money?
benefit, differ, die, refrain, resign, result, stem, suffer
They died from exhaustion.
arrive, believe, belong, confide, dress, interest, result, specialize, succeed
This chair belongs in that room.
conceive, die, dream, hear, think
You can only dream of a house like that!
agree, call, comment, concentrate, decide, depend, elaborate, impose, insist, lecture, live, operate, preach, rely
They agreed on a new treaty to ban nuclear weapons.
The current system will be phased out over the next two years.
add, adjust, admit, agree, answer, apologize, apply, attend, belong, confess, conform, consent, contribute, object, react, refer, resort, speak
They’ve agreed to the terms of the new contract.
agree, coincide, collide, comply, deal, fight, meet (with an accident), interfere, quarrel, speak, struggle, tamper
He agreed with her.
Some verbs can be followed by more than one preposition without a change in meaning:
He lectures on Italian literature at Columbia University.
He lectures about Italian literature at Columbia University.
If you are unsure which prepositions follow certain verbs, then look the verb up in a dictionary.