〜てほしい: want someone to do something
Separate wanting an object from wanting an action. Identify the actor, the object, and how direct your request sounds.
Move from wanting an object to wanting an action
新しい辞書がほしいです。 expresses wanting a new dictionary. 友だちに辞書を貸してほしいです。 expresses wanting a friend to lend you a dictionary.
Attach ほしい to a te-form: 教えてほしい or 待ってほしい. For a past wish, use a form such as 待ってほしかった.
Separate the person from the object
In 先生にこの漢字を教えてほしいです, 先生に marks the person you want to teach you, and この漢字を marks the content. The wish is usually the speaker’s.
私はこの漢字を教えたいです。 instead says that you want to teach this kanji. When switching between たい and てほしい, check who performs the action.
Expressing a wish can sound like a demand
もっとゆっくり話してほしいです。 expresses wanting someone to speak more slowly. Addressed directly to that person, it can sound demanding.
For a request, also learn もう少しゆっくり話してもらえますか, which asks whether they can do it for you. Adding です alone does not always soften てほしい enough.
Quick check: In 友だちに写真を送ってほしいです, does the speaker want the friend or the speaker to send the photo?
Show the answer and why
The friend. 友だちに marks the actor and 写真を the object to send. The sentence does not say the speaker wants to send it.