Make a small computer using Intel chips
Yes, of course, however it will take a lot of effort (and a bit of money.) Nowadays you would most likely use a microcontroller just because you need far less peripherals, and you could get it completed so much faster and cheaper. 

This is a crazy article, Man builds computer from scratch, including the CPU! Here is the original link, thanks to Kaz.

This is pretty much exactly what your asking about, William's Homemade Computer. It runs on an old Intel 486DX @ 20 MHz. I'm not sure if the software is complete, but it looks quite cool!




  But consider If I want to make a operation at 500MHz speed, what
  should I do?


Update Yes you can, although it would require a lot more work since at high speeds there are many more things to worry about, like impedance, matching trace lengths, noise, etc. However like I said you can. There are many new devices made that use an Intel Atom processor and operate in the Ghz range.

For something running that speed, you would need to have a printed circuit board made, and assuming you're using an Intel processor, you would need to have the whole chipset, memory, etc. on that PCB. I really don't recommend it. You could probably get an older mother board and play around with it, otherwise you basically have to create it all on your own and that is just a lot of time, money and effort.

However if you use a 32bit ARM instead of an Intel processor, it would be completely doable and not too expensive. Something like the Raspberry Pi is a fast computer that runs at about that speed and only costs $35 USA. It would of course be more expensive to make your own, but not too much.



Take a look at How to build an 8-bit computer from scratch. The picture looks like a wiring mess from hell!



Take a look at some of these videos:


Homemade mini i86 DOS computer with propeller chip for io's
How to Build a Computer ... from scratch
Homemade 6809 computer plays blackjack!
Homemade computer





  In old time how could people like Steve Jobs come up with new
  computers, designed by themselves. He didn't have any chip design
  company like Intel. Then how could he arrange the chips necessary for
  his computers?


He used ICs and processors to make the first computer in his parents garage, Apple I. In fact the Apple I was a fully assembled circuit board containing about 60+ chips. However, to make a working computer, users still had to add a case, power supply transformers, power switch, ASCII keyboard, and a composite video display.



You can buy/build a replica of that computer nowadays for ~$200 USA. Take a look at the Replica 1.



Some pictures of Steve Job's first computer, from here:







You may want to take a look at the history of computers.