a bit surprised also on the general question posted here, when so much information can be easily found on the subject with Google.
As to how they can be built, do some reading on the Finite State Machine as one technique that can be implemented by program logic arrays as the basic building block to control data paths, ALUs and other core functions of a processor.
Microcoded (or picocoded as we called them in IBM) processors have been around for a long time. It was the design philosophy that IBM used to build the System 360 family of mainframes 50 years ago, each with a unique processor optimized to a given level of cost/performance, yet each could run the same instruction set.
The floppy disk drive that became common in early personal computers was a derivative of the early, larger sized IBM 23FD Diskette Drive, the "Minnow" floppy drive used to load the pico code into the mainframe processor as part of the power up process.
The 360 Models 44, 75, 91, 95, and 195 were truly hardwired processors, which became increasingly difficult to do as logic technologies went from disretes to large scale integration.
The core of IBM 3705 communications controller was a hardwired processor as well as one it its high performance line protocol multiplexors.
A truly hardwired processor is a screamer in performance, compared to a pico coded processor designed from the same vintage technology; so not suprisingly the larger 360 models listed above were scientific/research machines of the era. You'll see quite a few Model 75s in 1960's era NASA pictures of their computers used to support the space program.