The phone was 2.5 years old, rather than junk it (since it couldn't be charged without the cable), I decided to attempt this repair. Now, I can either sell is as a working phone, or let another family use it as an iPod Touch. Haven't decided yet.
I have a little experience with minor electronic repairs - replacing hard drives in my MacBook Pro, replacing the screen in an old PowerBook. So, I'm no expert, but I've done a little.
With that as background, I found this repair quite simple with the instructions and photos on iFixit. No real tricks to convey - just a straightforward repair. It took me less than an hour.
I found the use of a lamp with a magnifying glass attached VERY helpful for all the small screws. It probably wouldn't have mattered 15 years ago when my eyes were better.
The symptom for the iPhone was that it didn't recognize ANYTHING related to the cable - no charging, no communication via USB.
However, I noticed that as I cleaned the connector on the iPhone (cleaning was the first remedy I was going to try), one of the metal tabs that are part of the connector, actually came out with the toothpick I was using to clean. I'm talking about the tiny metal tabs that are the 'pins' of the 30 pin connector - the parts in the 30 grooves of the plastic.
This convinced me that the connector was the problem - that it was not software related. I guess the pins must have just worn down with 2.5 years of use and were starting to break and fall out. Based on my usage pattern, I expect this was over a 1000 connects/disconnects, which doesn't seem like a very long duty cycle. It was in a pretty humid environment, perhaps that contributed?
Note to others: depending on which pins broke first, I expect a user would experience different symptoms. If a pin related to charging broke first, the phone might not charge, but might still be able to communicate via USB. Or visa versa.