「手伝います」(てつだいます/tetsudai masu)= I help you. (a little polite)
「お手伝いします」(おてつだいします/otetsudai shimasu)= I help you. (more polite)
「手伝いましょうか?」(てつだいましょうか/tetsudai masyou ka)= Can I help you? (a little polite)
「お手伝いしましょうか?」(おてつだいしましょうか/otetsudai shimasyou ka)= Could I help you? (more polite)
「手伝わせてください」(てつだわせてください/tetsudawasete kudasai)= Let me help you.
「お手伝いさせてください」(おてつだいさせてください/otetsudai sasete kudasai)= Let me help you.(polite)
「私にそれ、やらせて頂けませんか?」(わたしにそれ、やらせていただけませんか/watashini sore, yarasete itadakemasen ka)= Could you make me do that?
〔 following the words of "私にそれ、", it is better that you are pointing the thing.
# you can change words sorting into [watashi ni yarasete itadake masen ka? sore]. following the words of [sore], it's better that you're pointing the thing. 〕