How do you deal with bad weather?

I'd love to transition from mostly commuting on the bike to always commuting on the bike, but I'm wondering how people deal with bad weather? I have a long commute and don't always have access to showers or anything when I arrive.

Is it having good water-proof bike gear, packing a change of clothes, or both?

If you pack a change of clothes, do you get back into wet clothes on the way home?

Cheers