This is a polite way to offer help or a service to someone else. When you say ましょうか, you're essentially saying 'Shall I do it?' and you're waiting for the listener to agree or give permission. It's a kind and cooperative expression, often used when you see someone who might need help or when you want to do something for them.

In conversation, it's very natural and common. You can use it with friends, colleagues, or strangers in polite situations. The response from the listener could be 'はい、お願いします' (yes, please) or 'いいえ、大丈夫です' (no, it's okay). The pattern is not used for asking about the listener's own actions—that would be ましょうか with a different meaning (e.g., 'shall we go?')—but here the subject is 'I'.

Remember to use the ます-stem, not the dictionary form. For example, from 手伝います (help), the stem is 手伝い, so you say 手伝いましょうか.