I'm trying to insert a flash object into ppt. I used Developer->Controls->More and selected the Shockwave Flash control, drew a box, selected Properties from the right-click menu. There is no apparent way to figure out what all those field choices do. I put the swf in the same folder as the ppt file and put its name in the SRC field and put True in the autostart field, but nothing happens when I run the slide in Slide Show.

How do I get the swf to play?

Not familiar with PowerPoint 2007 because I'm on 2010.
Perhaps you can read this tutorial on "How to insert SWF file into PowerPoint 2003/2007".
Good luck.

I initially used that same tutorial. The steps in the tutorial you suggest are exactly the steps I followed up until they began describing steps that aren't available in ppt 2007.

There's a statement midway in the tutorial that says "The next actions are the same in both versions." This is not true. Many of the steps following that statement aren't available in ppt 2007.

What you see in Properties doesn't depend on the version of Office it depends on the version of Flash Player so that may be the confusion.
Basically you need to enter the full path to the swf in Movie or URL whichever is there. Note that 2007 is buggy about embedding swf and it will probably stay linked no matter what you select.

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Buggy isn't the proper word. "Nonfunctional" is more like it.

I tried adding the full path to the swf media in all of the possible places (SRC, url, whatever) in various combinations; nothing works.

This is a non-documented, poorly conceived media function! Other media can be added in a very straightforward fashion, under the "Insert" tab.