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.

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

Cursed Totem stops players from activating mana abilities of creatures.

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.