The word to is frequently used with a verb infinitive, but it is not an essential part of it.
When an infinitive is used without to it is called a bare infinitive.
1. The infinitive is used without to after certain verbs like bid, let, make, see, hear, need, dare etc.
2. The bare infinitive is also used after the MODAL VERBS will, would, shall, should, may, might, can, could and must. (these are also called "auxiliary" verbs) They can ONLY be used together with another verb.
3. The infinitive is also used without to after had better, would rather, sooner than and rather than.
Remember we use the bare infinitive
We use gerunds (verb + ing):
2. After prepositions - I drank a cup of coffee before leaving. I read a book while leaving.
3. As the subject or object of a sentence - Swimming is good exercise. Walking is good for your health. Seeing you reminded me how much I had missed you.
We use 'to' + infinitive:
These are typical verbs followed by 'to' and the infinitive.
See further examples here