In order to be able to cast Epic spells, the following criteria must be met:

Caster must be lvl 21+ sorcerer, wizard, priest or druid
Spellcraft NWP if arcane caster, Religion NWP if divine caster (for every slot you have in Spellcraft and/or Religion you may cast one Epic spell daily, and it is not possible to have more than 5 slots in either NWP)
Epic Spellcasting feat

In order to choose Epic Spellcasting feat, you must meet the following criteria:
Able to cast lvl 9 arcane spells or lvl 7 divine spells
Spell Penetration feat
Greater Spell Penetration feat
Epic Spell Penetration feat
At least one meta-magic feat
Must be introduced to Epic Spellcasting by an Epic Spellcaster

Casting an Epic spell:
Spellcraft/Religion check DC 40
(add +2 to your roll pr. slot you have)

Save DC vs Epic spells:
20+caster’s level+any relevant modifiers (such as sorcerers’ cha mod etc.)

Epic spells can bypass Antimagic Fields:
The field saves vs the spell to try to block it – roll 1d20+20 vs DC 11+lvl of epic caster