I have a person living in my basement who helps with the mortgage payment. What are the rules for having to declare this as income?

If you're renting the room at fair market value, you must declare the income as rental income. You could then also claim rental expenses.

If your tenant isn't paying fair market value, you're in a "cost-sharing" scenario. In a cost-sharing scenario, you do not have to declare the payments you receive from the tenant, but you also can't claim any rental expenses, no can the tenant claim any benefit from rent paid, like the Ontario Trillium Benefit or other benefits that consider rent payments.

You can find more about this on the CRA's website: https://www.canada.ca/en/revenue-agency/services/tax/businesses/topics/rental-income/renting-below-f...