trauen
to trust
To place trust in someone; to believe that someone is honest and reliable.
Nach der schlechten Erfahrung traut sie niemandem mehr.
After the bad experience, she doesn't trust anyone anymore.

to trust / dare / marry
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to trust
To place trust in someone; to believe that someone is honest and reliable.
Nach der schlechten Erfahrung traut sie niemandem mehr.
After the bad experience, she doesn't trust anyone anymore.

You can recognize the meaning of 'trauen' from the grammar. 'Jemandem trauen' (to trust someone, with dative) means to trust. 'Sich trauen' (to dare, reflexive) means to have courage. 'Jemanden trauen' (to marry someone, with accusative) means to perform a marriage ceremony.
Ich traue meinem besten Freund vollkommen.
I trust my best friend completely.
The verb 'trauen' is closely related to the noun 'das Vertrauen' (trust, confidence) and 'die Trauung' (wedding ceremony). All of these words have to do with belief, bonds, and reliability.
Vertrauen ist die Basis jeder guten Beziehung.
Trust is the basis of every good relationship.
When 'trauen' means 'vertrauen' (to trust), the person you trust is always in the dative. A common mistake is using the accusative.
Kann man diesem Politiker wirklich trauen?
Can one really trust this politician?
In the meaning 'Mut haben' (to have courage), 'trauen' is always reflexive ('sich trauen'). It is usually followed by an infinitive construction with 'zu', which describes what someone dares to do.
Sie traut sich, ihre Meinung offen zu sagen.
She dares to state her opinion openly.
When an official person marries a couple, 'trauen' is used with an accusative object. The subject is the person conducting the ceremony (e.g., the priest), and the object is the couple.
Ein Kapitän darf auf hoher See Paare trauen.
A captain may marry couples on the high seas.
to marry / to marry off
'verheiraten' and 'trauen' can both have to do with a marriage ceremony. 'trauen' is used especially for the person who officially performs the marriage, for example a registrar or a priest. 'verheiraten' can mean that someone arranges or brings about a marriage for other people; in the form 'sich verheiraten', it means to get married oneself. The words can be confusing because both occur in the context of weddings. As a simple guide: the couple 'heiratet' or 'verheiratet sich' (gets married), while the registrar 'traut' the couple (marries the couple officially).

Im Rathaus hat die Standesbeamtin das Paar am Freitag getraut.
At the town hall, the registrar married the couple on Friday.
In manchen Familien wollen die Eltern ihre Kinder noch sehr früh verheiraten.
In some families, the parents still want to marry off their children at a very young age.