"[Type]cycling [cost]" means "[Cost], Discard this card: Search your library for a [type] card, reveal it, put it into your hand, then shuffle." This type is usually a subtype (as in "Mountaincycling") but can be any card type, subtype, supertype, or combination thereof (as in "basic landcycling")
The same is true for +1/+1 counters
They also have willpower just like characters
The specific ruleset (or format) played at prerelease is called Sealed, and thats what youll be playing for the Final Fantasy event too
To help, you have several versatile songs and actions
A three-cost card, Mama Odie, Mystical Maven is a good card primarily because of its cheap cost and ability: This Going to be Good