Quick answers
How do I heal quickly in Terraria?
Press H to use the best healing potion in your inventory, J for mana and B for every buff potion at once. On controller they are on the D-pad.
How do I use a grappling hook?
Equip it in the hook slot and press E aimed at the mouse; on controller press Triangle/Y. Hooks work through gaps and pull you to the cursor point.
What is smart cursor?
Left Ctrl toggles it: mining, placing and hammering target the most sensible block near the cursor instead of the exact tile. Turn it off for precise building.
How do I mount?
Equip a mount item in the mount slot and press R; press again to dismount. Mounts stay until you leave them or take a hit that dismounts.
How do I zoom the map?
Press M for the full map, then + and - or the mouse wheel to zoom; Tab cycles the minimap style.