Here's an link on having a custom chip made: http://electronics.stackexchange.com/questions/7042/how-much...
getting chip done cheap: http://www.planetanalog.com/author.asp?section_id=526&doc_id...
computer built with transisters: https://hackaday.io/project/665-4-bit-computer-built-from-di...
IC built from scratch: http://hackaday.com/2010/03/10/jeri-makes-integrated-circuit...
or with unlimited money buy one of these: https://en.wikipedia.org/wiki/List_of_integrated_circuit_man...
"Hydrofluoric acid... 1000 degree oven... a child can do it..."
Lol. Yeah, I encourage using 3rd-party fabs on visually-inspectable processes for the individual components for a reason. Doing it by hand at transistor level can friggin kill you. Still neat stuff to learn, though.
You can get much of the knowledge you need from books, CPU specs, academic papers, open-source CPU's in industry, and so on. The standard cell model is the easiest with the highest performers being full-custom designs. There are plenty of successful designs in former with good performance, though. So, that's you're best bet.
Here's a GPL one used in embedded (esp space) applications for you to start with that has good performance and extremely-high configurability:
http://www.gaisler.com/index.php/products/processors/leon3
Recent one for open ISA:
https://github.com/ucb-bar/rocket
Lots of interesting things might be done with asynchronous logic that's not as explored and patented compared to synchronous techniques. The cutting-edge stuff is using it more and more. Whole chips have been done that way that were easier to fab right the first time plus with energy and performance benefits.
http://vcl.ece.ucdavis.edu/asap/
Are you starting from beach sand, or do you have a fab and raw materials? There was an interesting video that showed what you had to do to make a pencil "from scratch".
The big surprise line is that there's no one on earth who knows how to make a pencil. (It therefore serves as testimony in favor of free enterprise and against the idea of a centrally planned economy.)
You could build a CPU with a copy of the book and a big box of transistors, wires, breadboards etc.
I'm still working through the book, but I've learned a ton.
Implement your own hardware, make a compiler for your own CPU , memory controller, and so on...
VHDL/Verilog and KIT goes a long way. I would vouch for de0 nano from altera.