Actually, my University had a class where students would design and fabricate an IC. They had to wear the cleanroom jumpsuits, deal with the toxic chemicals, and everything. The lab was very locked, but you could see people working inside the window and they would put chips students had made in the window. I don't know whether, or how, they got them packaged.

Problem is, whatever they did to afford this for that class, they were amortizing the costs over all of the students taking it each term. You don't just print out an IC. You have to zap a whole wafer, then cut it, then package it. The process is very expensive.

So, why can you get chips for cheap online?

• The actual silicon for the cheap chips is tiny. They fit hundreds if not thousands on a wafer. (So you're SOL if you only want, say, 10 of whatever it is. Gotta do the whole wafer.)
• They have industrial machines set up to automatically roll out wafer after wafer of the things, so they get to set up an industrial wafer cutter once and then just let it do its thing, dividing the cost of that equipment over millions or billions of sold units. The cutting has to be extremely precise, though I suppose you could make that easier by wasting wafer space.
• They get to set up testing equipment once, and then it just stamps down on wafers all day and verifies that their contents work. Again, that cost gets divided over millions or billions of sold units.
• Same with the packaging. Cost of a big, automatic, industrial machine gets divided over lots of units.

So say you were to call up a fab facility and ask to do a custom run of a chip you made. You're going to print one wafer full of chips, minimum, because that's how that works. So you're paying for the wafer, not for ten chips. Then they will need to adjust their cutting equipment just for your one wafer. Then the problem of testing comes up... There's no way you're getting one of these things to make your testing efficient, the way the big dogs do it. You'll probably just package all of the chips on your wafer, and then test after packaging. Which brings us to packaging... I honestly don't know what you can and can't do with the big, professional equipment there. I don't know if you can just program a computer to wire IC pads to package pads and let it go on whatever chip you place under the machine. If you can, that's awesome. (But you're still paying for that programming and setup, spread over your run of 10 chips). If you can't, well I wouldn't even want to think about how long it would take a guy to do that manually. And that guy won't work for cheap!

Dave's EEVblog #532 gives a great glimpse into the fabrication process and the tools required to work with it. Highly recommended if you haven't seen it.