The physical specification is based on the Eurocard standard of: 3U (5.06 inches or 128.5 mm), where height "U" is measured in rack units, rounded for a lip (nb: 3U in standard rack units would be 5.25 inches or 133.3 mm). 1HP (0.2 inches or 5.08 mm), where width "HP" is measured in horizontal pitch units. The modules are generally about 2.5 to 3 inches deep, but this part of the standard is not well controlled. Each vendor generally makes the module depth to suit their own board space needs.
The mechanical Euro "rack" into which the modules are assembled, is often referred to as a "Boat" or "Skiff" because that is what an empty rack looks like in minature. These "Eurorack" cases can be fairly expensive, so I look on Etsy for the best deals. Eurorack cases on Etsy
If you want to make your own Eurorack Synth modules, you might want to consider making the front panel out of metal from "Front Panels Express", using their own design software "Front Panel Designer". This can be fairly expensive in small quantities, but you get very professional looking results. The other way is to make a PCB with the silkscreen designed for marking the control functions. This means using KiCAD, and ordering the boards from China, which can put PCBs in your hands in a few days. (My last order only took 4 days to boards in hand.)
Synth Cube has a wide range of Eurorack modules, both finished and kit form, from many vendors.