I am a US Green Card holder. Do I need a visa to travel to and from Canada?

From The Government of Canada website:

As a U.S. Green Card holder, you do not need a visitor visa to travel to Canada. However, you are expected to have an eTA if you plan to fly to or transit through Canada.

When flying to Canada, you will need to present:

• proof of status in the U.S. (such as a valid Green Card), and your
• valid passport that you used to apply for your eTA. The border services officer will verify your eTA when you arrive in Canada.

When travelling by land or sea directly from the U.S., you will only need to provide proof of your U.S. lawful permanent resident status (such as your Green Card).

I am a US Green Card holder, do I need a visa to travel to and from Canada?

No, but if you're flying to Canada you will need eTA. If you're not flying, you don't even need a passport; you can use your green card by itself in both directions.

Also my friends are US citizens; can they use birth certificates to enter and depart from Canada?

If they're traveling by land, they can use their birth certificates to get into Canada, but they will also need additional identification, such as a driver's license. Canada seems to be making this information difficult to find on their website. I presume it is hard to find because to get back into the US, they're supposed to have a WHTI-compliant document, and Canada does not want to be seen as undermining US law.

WHTI-compliant documents are:

a valid: U.S. Passport; Passport Card; Enhanced Driver’s License; Trusted Traveler Program card (NEXUS, SENTRI or FAST); U.S. Military identification card when traveling on official orders; U.S. Merchant Mariner document when traveling in conjunction with official maritime business; or Form I-872 American Indian Card, or (when available) Enhanced Tribal Card.

In practice, a US citizen can't be denied entry into the US, but getting in without a WHTI-compliant document can be problematic and time consuming and is generally not advisable. The US government says

What if I don’t have the required documents when I travel to or return to the United States?

Travelers without WHTI-compliant documents are likely to be delayed at the border as CBP officers work to verify identity and citizenship.

The US State Department says of Canadian entry requirements:

Canadian law requires that all persons entering Canada carry both proof of citizenship and proof of identity. A valid U.S. passport, passport card, or NEXUS card satisfies these requirements for U.S. citizens.

Children under 16 need only present proof of U.S. citizenship.

The first sentence implies that a US birth certificate and driver's license should suffice.

Canada, for its part, says:

American citizens, including American-Canadian citizens, must carry proper identification and meet the basic requirements to enter Canada. You do not need a Canadian passport, a Canadian visa or an eTA to enter Canada if you are travelling with a valid U.S. passport.

Following the "carry proper identification" link leads to a page that avoids saying that US citizens must carry a passport. They recommend a passport, and they note, for example, that travelers "may" use certain other documents, but they never present an exhaustive list of acceptable documents, nor do they mention any unacceptable documents.

If your friends are flying, they'll need passports or NEXUS cards.

No, you don't Need a visa.

If entering by air, you need a passport with an eTA and the green card.

If entering by land or sea, you just need the green card (so not even a passport).

Your friends can use a passport or NEXUS card by air, and any proof of citizenship by land (though it's recommended to have either a passport, passport card, enhanced driving licence or NEXUS/FAST/SENTRI card)