〜させてください
please let me
Causative て-form + ください / もらえませんか
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The causative て-form + ください asks permission to do something yourself: 今日は早く帰らせてください, "please let me go home early today". Literally "please make/let me go home".
It's the standard polite way to ask to be allowed to do something, and it also frames offers humbly: 私にも手伝わせてください, "please let me help too". ちょっと考えさせてください, "let me think about it", is a polite way to not say yes right away.
Softer still: させてもらえませんか or させていただけませんか, "would you let me…?"
Don't mix it up with plain てください: 帰ってください is telling the other person to go home.
Examples
今日は早く帰らせてください。
Please let me go home early today.
ちょっと考えさせてください。
Let me think about it for a moment.
私にも手伝わせてください。
Please let me help too.
一言言わせてください。
Let me say one thing.
写真を撮らせてもらえませんか。
Would you mind if I took a photo?