After flowering you can cut the stems back and the whole plant will usually brown off and disappear until next year - well mine do in this awful climate of ours!

Prune is not a word I would use about the agapanthus plant. I grow mine in a large pot in which, over the years, they become pot bound and flower the better for it. I do water well in the summer months. When the flower heads have died I usually cut down my flower heads but if you leave them the seeds on the heads do look attractive. About november the leaves become brown and a bit mushy...about this time I gently pull them away and clean the plant up. I have always found the agapanthus quite hardy but I do carry the pot close to the house during winter months. I have never grown them directly in the garden- Always preferring pots. I do love my Northern Star - look out for it.
Philip.