This is a wide open question, not sure where you want to go with it. Wikipedia covers the generic topic with a generic answer. The native code being emulated or virtualized is replaced with native code. The more the code is run the more is replaced.
I think you need to do a few things, first decide if you are talking about an emulation or a virtual machine like a vmware or virtualbox. An emulation the processor and hardware is emulated using software, so the next instruction is read by the emulator, the opcode pulled apart by code and you determine what to do with it. I have been doing some 6502 emulation and static binary translation which is dynamic recompilation but pre processed instead of real time. So your emulator may take a LDA #10, load a with immediate, the emulator sees the load A immediate instruction, knows it has to read the next byte which is the immediate the emulator has a variable in the code for the A register and puts the immediate value in that variable. Before completing the instruction the emulator needs to update the flags, in this case the Zero flag is clear the N flag is clear C and V are untouched. But what if the next instruction was a load X immediate? No big deal right? Well, the load x will also modify the z and n flags, so the next time you execute the load a instruction you may figure out that you dont have to compute the flags because they will be destroyed, it is dead code in the emulation. You can continue with this kind of thinking, say you see code that copies the x register to the a register then pushes the a register on the stack then copies the y register to the a register and pushes on the stack, you could replace that chunk with simply pushing the x and y registers on the stack. Or you may see a couple of add with carries chained together to perform a 16 bit add and store the result in adjacent memory locations. Basically looking for operations that the processor being emulated couldnt do but is easy to do in the emulation. Static binary translation which I suggest you look into before dynamic recompilation, performs this analysis and translation in a static manner, as in, before you run the code. Instead of emulating you translate the opcodes to C for example and remove as much dead code as you can (a nice feature is the C compiler can remove more dead code for you).
Once the concept of emulation and translation are understood then you can try to do it dynamically, it is certainly not trivial. I would suggest trying to again doing a static translation of a binary to the machine code of the target processor, which a good exercise. I wouldnt attempt dynamic run time optimizations until I had succeeded in performing them statically against a/the binary.
virtualization is a different story, you are talking about running the same processor on the same processor. So x86 on an x86 for example. the beauty here is that using non-old x86 processors, you can take the program being virtualized and run the actual opcodes on the actual processor, no emulation. You setup traps built into the processor to catch things, so loading values in AX and adding BX, etc these all happen at real time on the processor, when AX wants to read or write memory it depends on your trap mechanism if the addresses are within the virtual machines ram space, no traps, but lets say the program writes to an address which is the virtualized uart, you have the processor trap that then then vmware or whatever decodes that write and emulates it talking to a real serial port. That one instruction though wasnt realtime it took quite a while to execute. What you could do if you chose to is replace that instruction or set of instructions that write a value to the virtualized serial port and maybe have then write to a different address that could be the real serial port or some other location that is not going to cause a fault causing the vm manager to have to emulate the instruction. Or add some code in the virtual memory space that performs a write to the uart without a trap, and have that code instead branch to this uart write routine. The next time you hit that chunk of code it now runs at real time.
Another thing you can do is for example emulate and as you go translate to a virtual intermediate bytcode, like llvm's. From there you can translate from the intermediate machine to the native machine, eventually replacing large sections of program if not the whole thing. You still have to deal with the peripherals and I/O.