The list
The Canada Revenue Agency keeps the List of Charities. Search it by name or by business number. A registered charity's number ends in RR0001, and the entry shows whether it is currently registered, when it was registered, and what kind of charity it is. If a charity is not on the list, it cannot issue an official donation receipt, whatever its website says.
What the annual return tells you
Each charity files a return with the CRA every year, called the T3010, and the list shows it. It describes the charity's ongoing programs in the charity's own words, and it breaks down where the money came from and where it went. You do not need to read all of it. The program descriptions and the year are usually enough to tell whether the organisation is doing what its website says.
How a receipt works
Only a registered charity can issue an official donation receipt, and the receipt carries the charity's business number. When you give through CanadaHelps, CanadaHelps takes the payment, issues the receipt on the charity's behalf, and sends the charity the gift. Keep the receipt for your return; the charity does not need a copy.
Us, as the example
Our business number is 778365528RR0001. Search it on the CRA list and you will find Lighthouse Training Center, status registered, designation charitable organization, effective 24 December 2020. The return lists our ongoing programs as training in information technologies, tax returns preparation, translation, and teaching Microsoft Office. Donations to us go through CanadaHelps, which issues the receipt. The link to the register is on our About and Donate pages.