Tools needed: Adobe Photoshop 6 (US$609)
Photoshop is simply the most effective tool for the job. I will describe in this tutorial my process for creating morphs step-by-step in Photoshop 6. (Sorry if this seems a bit snobbish to those of you without a spare $609, but you can't drive in the Indy 500 in a Chevy Cavalier). If you have access to the funds, you should support Adobe's amazing product and purchase the full version, or pretend to be a student and buy the cheaper educational version. Please don't use or distribute pirated versions; it will discourage Adobe from funding future versions of a great program.

Update: Adobe releases Photoshop 7, with improved Liquify function.

Your alternative is to buy ScanSoft SuperGoo (the sequel to the respectable Kai's Power Goo, US$19.99), and a cheaper photo-editing program (like Photoshop Elements, US$99). You can then do as I used to: morph in Goo, then masking and touchup in the imaging program. I hear that Corel Photopaint works pretty well also, but I can't vouch for it. You can apply many of the principles in this tutorial with other software, but I'll be describing the steps as they work in Photoshop 6.

1. Pick your image
Clothed vs nude: I cheat a little by working only with clothed subjects. It makes for a lot less work for the realism I like to create. I'm not saying there aren't convincing nude morphs out there, but they take more time than I want to spend. The fact that I prefer seeing recognizable celebs with huge knockers is only a convenient side benefit : )

Size: I cheat a little more by working at a large image size and scaling down the final result. I usually morph an image that is 1200 pixels tall, and drop it down to 600-700 tall for the final product. This helps to hide distortions from the morphing in the final image.

Clothing: To minimize visible distortions, the subject should be wearing an unpatterned top, or one with a very busy, random pattern. Beaded gowns are out: when the size of the beads is changed by your morphing, the result is unrealistic. Repeating patterns, like plaid or polka dots, can also be trouble.

Position: "3/4 view" of the subject is best (view from the front, at an angle, so one side is in front of the other). Straight front works almost as well, but too much of a side view can be hard to get the cleavage right.