It didn't go smoothly. After the happy splash screen, I tried to log in to my account. The result was an error message displaying this text:
No Network Connection
Please check your network settings
and try again.
Wristlock reported that he got past that error message by rebooting his iPhone. I rebooted, tried again, and my log in succeeded.
The proof of the pudding is in the voice call, so I called the lovely Skype Test Call woman. She let me down: she echoed a little, and her voice dropped out a bit. I told her a secret, and my voice came back with dropouts. Overall, the call quality was poor. Worse, Skype crashed during my test calls and immediately after my voice echoed back.
But wait! iPhone Hacks reports that the instability only occurs on jailbreaked iPhones, and Saurik already has a fix. I ran Cydia and updated Mobile Substrate. I rebooted the iPhone and tried Skype again. Audio was still a bit jittery during the short test call, but on a longer call to a coworker in Europe, the audio was good enough. Better yet, the Skype app didn't crash during our 10 minute conversation.
The bottom line: Skype for iPhone works fine. Use it as your mobile Skype client or as a backup when your PC crashes.