Druids are fairly easy pickings for a combat shadow priest.  Always open a fight with a druid with a blast followed by several dispel magics.

Druids use a lot of debuffs, therefore remember to dispel magic on yourself.

When the druid hits about 1/3 life, they will cast their big heal. Wait for that moment to silence them.  Then immediately follow up with a Mind Blast. Feast on their primary-healer-wanna-be-corpses.  If your build does not have silence, be prepared for a long fight.  Keep your health up and conserve your mana. Do not put plague on the druid, he can cure it, but keep pain on them. Try to use your fear as early in the fight as possible so that it will be available when the druid morphs for healing.  Be very close to the druid when he morphs out, and fear him then (in leue of silence), then unload as much damage as possible on the druid. If you are quick enough, the druid will fall.  If not, run until your mana is back up, then try again. 

If the druid is Tauren, be wary of them when they morph into caster form.  A good druid will try to morph, then war stomp, to allow themselves time to cast their big heal while you are stunned.