Canadians
Canadian citizens do not require O or P visas to enter the U.S., but do require approval from the USCIS. Canadian permanent residents (landed immigrants) DO require visas, as do all third-country nationals (those not from the U.S. or Canada) entering the U.S. from Canada. Canadian citizens need simply present themselves at a port of entry or pre-flight inspection location with proof that USCIS has approved their O or P classification. If the petition has been approved, the computer system will contain a full record of that approval, but the best proof remains an I-797 Approval Notice - ideally the original rather than a copy.
As a precaution, always provide the alien with a full copy of the underlying petition. Otherwise, though, there are no applications as such or visa fees if visas are not required. Note that all U.S. Customs and Border Protection (CBP) personnel can quickly access approval information once entered into the system, so it is not common practice for a CBP inspector to refuse to admit an alien who does not require a visa simply because s/he lacks the original, or even a copy, of the I-797 approval notice.
Canadian nationals or permanent residents applying through land ports of entry -- in fact anyone who is entering the U.S. through a land port -- are advised to complete the provisional I-94 or they will not have any evidence that they were inspected upon entry. This is especially important in the event a future petition to extend might be filed, which would require proof of recent entry or expiration of current stay.