After certain auxiliary verbs

Infinitives are used without ‘to’ after the auxiliary verbs will, would, shall, should, may, might, do, did, can, could, must, need and dare.

I will invite them.
You shall go at once.
They must come.
It may rain.
You need not go.
He dare not ask.

Note that when dare and need are used as principal verbs, they are followed by the to-infinitive.

Did he dare to ask?
We need two months to complete the work.

After verbs like bid, see, hear etc.

Infinitives are used without ‘to’ after some principal verbs like bid, watch, see, let, make, help, hear etc.

I bade him come.
Let him sit down.
I saw him do it.
We heard her sing.
She helped him lift that box.
I watched them jump.

After rather, better and had better

Infinitives are used without ‘to’ after rather, better and had better.

I would rather wait.
You had better consult a doctor.

After except, but, save and than

Infinitives are used without ‘to’ after certain prepositions like except, but, save and than.

He does nothing all day except sleep.
She said she would die rather than surrender.

Notes

Bare infinitives can be re-written as to-infinitives.

She can knit. (=She is able to knit.)
I bade him go. (=I asked him to go.)
Let him come. (=Allow him to come.)
I must go now. (=I ought to go now OR I am obliged to go now.)
Better re-write this composition. (=It is better to re-write this composition.)