The granted abilities effectively use "this permanent" rather than "[that card's name]," so you treat the abilities as though they were printed on the creature that gained the ability. For example, say you exiled the card Argothian Sprite with Agatha's Soul Cauldron. Argothian Sprite has the ability ": Put two +1/+1 counters on Argothian Sprite." If you controlled a Callous Sell-Sword with a +1/+1 counter on it, you'd treat it as though it had the ability ": Put two +1/+1 counters on Callous Sell-Sword."

Agatha's Soul Cauldron grants only activated abilities. It doesn't grant keyword abilities (unless those keyword abilities are activated), triggered abilities, or static abilities.

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