Best for tea are the seeds, but they should come not from Florence or bronze fennel but from common fennel, the kind that grows as a weed in California and the Mediterranean region. The seeds will dry on the plant, but to keep them from dropping you may want to cut the stalks and hang them over a cloth before the seeds are dry. To make fennel tea, bruise the seeds before steeping them.
I haven't tried drying fennel leaves. Sarah Garland, in The Complete Book of Herbs and Spices, says that they're not suitable for drying but that the stems are. She says you can add the dried stems to winter dishes just as you might the seeds.
If I had Florence fennel go to seed, I'd save the seeds for planting the next year.