You can dig pretty much anywhere, and third shovel down you'll find clay. In the flatlands, pretty much every other village has (or has had) its own brick plant. Often they'd build one near the road, and then when the clay pit becomes a lake, or just too wide to reach with the wagonets, they build another one on the other side of the village (using the last bricks produced in the first one, of course).
The quality of the brick is, well, good enough. The bricks may vary in size by a millimeter or two, a certain percentage will break in transport, and the sides may not be always smooth - which doesn't matter to the masons, the mortar will more than compensate.
That's for the cheapest, village brick. Then there are better ones, all the way to the red façade brick, yellow and rather white silicate brick. The latter two aren't plastered over.
There's the old format, which was around 3"x6"x12", but that's German inches (zoll), which are exactly 25 mm - not the American inches, which were "rounded" to 25,4 mm. The standard brick nowadays is 62,5 x 125 x 250 mm, i.e. four in a meter lengthwise.
Usually the bricks are bound by regular mortar (sand and lime), or, for stronger binding, the extended mortar (sand, lime and cement in a 9:3:1 ratio)... or you can get really inventive and do it in the most expensive (and flimsy) way: