I have a great idea for general consumer-use desktop application, but
I have no technical skills. How would I go about hooking up with a
programmer to develop it, and typically how much of a split would this
person require, considering they're doing the programming (I have the
idea the basic feature set, and would handle distribution).

I know this is all negotiatable but there must be a reasonable "range"
number you can give me.

Personally I'd be inclined to take a look at Elance
http://www.elance.com the professional services eBay - you can put a
job out to tender and software developers can bid for the work. Good
luck - developing the product is one thing, getting it to market is
another completely!

Another site you might consider is http://www.itmoonlighter.com.

If you believe in your idea enough and can afford it, you might
consider just hiring a programmer to develop the product without
sharing the revenue from sales.  If you do that and the product
succeeds, you make more, and you can select from all the programmers
who will work for cash, which may be a bigger universe than the
universe of those who will believe in your marketing genius enough to
invest their time on speculation.