Particular verbs (and adjectives) take particular kinds of complement, and there are few general rules.
Verbs of perception such see, hear, and feel, can take:
- a that clause: I saw that her eyes were starting to tear up.
- an infinitive clause without to: I saw her eyes start to tear up.
- a 'gerund' (-ing) clause: I saw her eyes starting to tear up.
- other kinds of complement which are not relevant here.
But they cannot take a to infinitive clause: not I saw her eyes to start to tear up.
Other words have different patterns: know can take a that clause, and a to infinitive clause, but not the other two kinds. (There's a special context where know in the perfect can take an infinitive clause without to: I have known him go there; but otherwise it can't), Understand can take a that clause, a to clause, or a gerund clause, but not an infinitive clause without to.
For the most part, you just have to learn what complements a particular word takes.