My dill bloomed and now I have seeds....do I need to do anything with them to make them grow next year?

I usually wait till the dill heads turn brown, then I just pull off the seed and scatter them where I want them to grow. Nothing else is needed. Next year you'll have more dill than you will know what to do with. Sometimes I get a handful of seeds and throw them over the fence in the neighbors yard. Enough dill for everyone.

I am a renter and I move often. Because of this I keep my horde of herbs in pots so I can move them with me. In fact, I'm moving again in about a month. If I bring the dill seeds inside and put them in a packet (so I don't lose them) will I need to put them in the fridge so they get a cold season, or soak them in warm water before I plant them?

No special treatment for dill seed is needed.