Cannot be Special Summoned, except by its own effect. After this face-up card on the field is destroyed and sent to the Graveyard, during the Standby Phase of the next turn: You can discard 1 card; Special Summon this card from the Graveyard.
The Supremacy Sun cannot be Special Summoned with other card effects so you will need to Tribute Summon him. Mausoleum of the Emperor lets you Normal Summon him at the cost of a lot of LP. Fires of Doomsday can Special Summon tokens to use as a tribute for summoning The Supremacy Sun.
Use Destruct Potion to destroy your own The Supremacy Sun and heal 3000 LP. The Supremacy Sun can then revive itself during the next Standby Phase. You can also do this to let The Supremacy dodge non-destruction removal which he cannot revive from.
The Supremacy Sun’s discard cost can trigger the effects of Fabled monsters. Fabled decks are also capable of Special Summoning lots of smaller monsters to use as tribute for The Supremacy Sun.
Aside from having an appropriate type and attribute, The Supremacy Sun is also good at emptying your hand so your Infernity monsters can gain their full effect. Infernity Avenger is a good discard option because his effect is only useful while in the graveyard. You can also discard Infernity monsters to use as cost for Infernity Break or to revive with Infernity Necromancer.