Wordlessly is the adverb: it tells you HOW someone did something — without saying anything. She wordlessly handed him the letter. He wordlessly pointed at the door.

The important part is that an action is still happening. Wordlessly is not the same as silently. 'Silently' is about sound — moving with no noise. 'Wordlessly' is about speech — you may make plenty of noise, but you don't talk. Someone can wordlessly slam a door, and that is loud but still wordless.

Because it always sits next to an action verb, it works hardest in storytelling. It carries a small weight of meaning: the silence itself is doing the communicating. 'He wordlessly took her bag' suggests he understood without being asked. 'She wordlessly turned away' suggests anger, or hurt, or refusal. That is why you meet it far more in novels than in conversation — in speech people just say 'without saying anything'.

Position is flexible: before the verb (she wordlessly nodded), after the whole action (she nodded wordlessly), or at the start of a clause. Before the verb is most common in modern writing.