How do I build my own computer/processor?

I want to build (or at least design) my own simple computer. Input and output are going to be extremely simple, possibly a grid of LEDs for output and switches for inputs. This includes building a very simple CPU from smaller components, maybe 7400 series TTL chips. How would I design such a computer? The most difficult part is probably the CPU, so how would I build one?

I know that the answer depends on what I want the computer to do. I want it to be able to do:
simple math (+, -, *, /)
binary operations (and, or, not)
run simple programs from ROM (ROM consists of switches)
take a one byte number from input, with an “enter” switch
use certian memory locations as output/input

I know the answer is complicated, so all I want is a link to where I might learn more about how to do this.