Not sure how experienced you are with digital logic, but I would start there. Start with combinational logic then sequential logic. Then move on to timing analy

Not sure how experienced you are with digital logic, but I would start there. Start with combinational logic then sequential logic. Then move on to timing analysis and basic pipelining. Then get a FPGA dev board and design some basic things like a simple processor. You could also use the FPGA as a more concrete way to test what you have learned in the aforementioned topics. Then once you get that down/understood. I would recommend looking at the papers and literature regarding the topics of interest and common architectures and structures. See what optimizations have been tried. The optimization targets are generally performance, power and space. Also with ASICs the standard cell libraries make things much easier since generally they are characterized pretty well. If you have the funds to make an ASIC that is. Still because that you spend most your time just verifying and testing your designs. -EDIT- If your thinking custom analog circuits your going to have to learn a lot more. Starting with circuit fundamentals, but your also going to need solid understanding of semiconductor physics. There is also the problem that outside simulation testing ideas/designs is quite expensive. Unless what you have is something that could be constructed out of discrete components. So unless you got a company or university backing you it's unlikely you would be able to make any physical prototypes. Although prices have been getting cheaper for older processes, and there are services like MOSIS.