Play Mid Morgana as a counter-pick against AP control mages or AD assassins, and Support Morgana as a utility pick to nullify enemy CC, not a damage dealer.
Maximize the potential of her core abilities: Q's long root and E's CC immunity. As support, after maxing Q, prioritize E if facing heavy enemy crowd control.
For Support Morgana, focus on utility items like Rylai's, Redemption, and Locket over damage items, utilizing W with Rylai's for consistent AoE slows to assist your team.