Activated abilities contain a colon. They're generally written “[Cost]: [Effect].” Some keywords are activated abilities and will have colons in their reminder text.

Cursed Totem doesn't stop players from activating abilities of creature cards that aren't on the battlefield, such as cycling or unearth.

Activated abilities of noncreature permanents that would make them become creatures (such as a Vehicle's crew ability) can still be activated. Once they become creatures, any abilities they have cannot be activated.

Cursed Totem stops players from activating mana abilities of creatures.

Other abilities of creatures, including static abilities and triggered abilities, are unaffected.