While there's still ample availability of cameras, film, and people to develop it, everybody should give crossprocessing a shot at least once! I've written about it before; it's a great way to force yourself to not shoot completely realistic pictures.
There's a lot of advice out there on this, but I found that much of it was somewhat questionable and different sources contradict each other, so I decided to write out how I suggest you approach crossprocessing.
You may like your first attempt at it, you may not. It took me a few rolls before I felt I had sufficent control over the process.
Make sure you have a place that will develop it. Nothing sucks more than getting all set up to shoot crossprocessing and not being able to do it, after you've already shot a roll and got your heart set on the funky colors
Sometimes you can get a one-hour lab to do it for you. Many of the pro labs will do it because their clients demand it, but some don't want to mess with their chemistry. If the lab discards their chemicals on a routine basis, you can always get them to run it right before they discard the chemicals and there's no risk of the chemicals getting messed up.
Kodak did some research that seems to indicate that it's OK to do a little crossprocessing, but I can't find that information on their current website.
Worst case, you can mail it to A&I
Get some slide film. One avenue is to go to a camera store and see if they've got some expired slide film for cheap. If you are buying new, try Kodak Elitechrome 100, Kodak E100G, Fujichrome Reala 100, or Fujichrome Provia 100F (I've seen the pro slide films be cheaper than the consumer slide films at places, so I list off both pro and consumer films)
Use a camera where you have some ability to control exposure settings. All you really need is the ability to manually set film speeds or exposure compensation.
If you don't have a camera like this, you still can be in luck, it just may take more rolls of film or more trial-and-error. If the camera automatically sets film speed, you can try and change the DX code and shoot several rolls of film. Or you may just be happy with it at the exposure it shoots by default.
If you have a camera with no exposure control, like a Holga, you will have very hit-or-miss results. Each film speed will work in only in one or two situations (e.g. 100 speed film in bright sunlight).
Bracket your shots by at least one stop in each direction. If you are changing the film speed, you want to set it to the film speed divided by two (So, 100 film would be 50) and the film speed multiplied by two (100 film would be 200). You can keep records, or you can always bracket in the same direction each time.
Develop the film and get your images from it. I usually scan the film. You can also have the lab print the images. Depending on the labs, they can control which adjustments are made. You often will want them to make contrast adjustments. Some people like the results from if you have them do all of the auto adjustments.... because the results from the auto adjustments trying to bring the picture back to normalcy are often quite interesting. I used to have them print it with no color adjustments but with contrast adjustments.
If you scan it yourself, there's a certain art to getting it to look interesting at all. I'm still working on the write-up for that.
Evaluate the results
Crossprocessing, I feel, is less about absolute correctness and more about aesthetics. I could write out a guide about how to judge a properly exposed and printed image, but everybody tends to like things looking a little different, so I won't. Go with what looks right to you.
Assuming that your camera manages exposure accurately, you will most likely discover that you prefer one of the three variations of film speed more than the other two. From now on, set your camera to that speed. You can repeat the bracketing tests again starting from the new film speed. You also might consider bracketing in smaller increments (If you like it at 100 speed, you could shoot at 64, 80, 100, 125, and 160 next time) to hone in on the correct exposure.
If you switch film types, you may have to repeat the process over again. If you switch developers, you may have to repeat the process over again.
Do try different films. I love using Elitechrome 400 (it's about the same as Ektachrome 400X) and Ektachrome E100VS. Some folks greatly favor EPP -- Ektachrome 100 Plus. Others like using some of the Fuji films. Old-style Kodak films like EPP tend to get grainy and have mostly accurate colors, new-style Kodak films like Elitechrome 400 and E100VS will have a different kind of hue to them and less grain, and Fuji films tend to have much less accurate (but still interesting) colors.