If you see a blind man having trouble crossing the street, offer him some assistance. Lending a hand is just one way of providing assistance.
Assistance is a noun that means to help or aid. It's the noun form for the verb to assist. Homes for the elderly are sometimes called "assisted living facilities" because they provide assistance to older folks who might need assistance getting in and out of bed, or feeding themselves. If you're in a store and no one is helping you, call a manager and ask for assistance. However, if you like to shop, you probably won't need any assistance spending money.