Can anyone tell me how to grind coriander seeds? Do you discard the shells or do they soften in baking?

Hmmmmmmm. Good question. I haven't used them in baking, so can't say.

For most applications I toast the seeds, then crush them in a mortar to the consistency I want. If I need a fine powder I'll use a spice mill.

I imagine you could do that: Grind them fine in a spice mill. I can't think of any reason why you should discard them.