Hello,
"Can/could" is a modal verb, like "must", "should", "will/would", "may/might", and "ought to". They are never followed by "to", except "ought to", which is an exception.
There is also no need to worry about the third person singular.
I swim. - He swims.
I can swim. - He can swim.
But there are some other verbs that are followed by so called "bare infinitive" (infinitive without to).
For example:
Make sb do something.
They made me lie on the floor.
The smell of roses makes me think of you.
Let sb do something.
Let’s go. (Let us go)
Please, don’t let him do it.
"Help" can be followed by either infinitive or a bare infinitive. I don’t know about any difference in meaning.
Help sb [to] do something.
She helped me to cross the road.
She helped me cross the road.
Any other questions are welcome.
Nikita Kovalyov
www.eclecticenglish.com