Harvesting Black Mustard

I would like to first apologise in advance for this stupid question, but I hope someone there will answer it. I have enthusiastically grown some black mustard this summer and it has produced seed pods in abundance. I have harvested and dried the pods on the stems. How do I now get the seeds out of the pods in the simplest way?

On the contrary, yours is a very good question!
Farmers use combines to swath and thresh at the same time. Threshing splits the pods and separates the seeds in one operation. Obviously, such equipment is not available to home gardeners.
At home, you could try several traditional methods of threshing. You could put the dried pods in a large cloth bag and beat the bag against a hard surface. It may require trampling on the bag and its contents with your feet to split the pods. You may have to play with the amount of material you put in the bag because too much may cushion the pods from impact and prevent pods from splitting. A sturdy plastic bag may work also. It is important that the pods be completely dry otherwise they may not shatter, and the excess moisture may eventually encourage molds to develop in storage.

How do I separate the seed from the chaff?

The seeds can be cleaned with a combination of methods. Screens of several hole sizes, along with an incline, are very helpful. If you have a screen with 3-5 mm holes, and a finer screen typical of windows, you can remove much of the chaff and dust. The remaining debris can be separated easily by rolling seeds down an 30 to 45 degree incline adjusted so most of the chaff stays on the incline and the seeds roll down.