Google Buzz is actually slightly more insane on Android phones and iPhone than the desktop: There's a revamped, Buzzier Google homepage and you can post entirely using your voice. Update: Hands on!
How Do I Get This Party Started?
First, a disclaimer: Right now, Buzz on the mobiles is working intermittently at best, and may very well be broke as shit. But it's better than it was right after launch. (Digression: If Google can't launch an internet service correctly, can anyone?) Also, iPhones and Android phones only. You might probably just wanna stick with Wi-Fi for now, too.
1. Sign into your Google account on yer phone, then go to google.com/buzz.
2. Your homescreen should look something like this. Let's follow some people! Click "following zero people", where you'll be prompted to stalk some of your friends.
3. Type someone's name to start searching: It'll give highest priority to your existing contacts. I just followed Herrman here.
4. Now let's see what's going on nearby. Oh hey, it's Herrman. Creepy! I'm going to comment and Like his status. He's at B-Cup Cafe, which I think kind of sucks. You can see it on the map here. Popping over to the listing, you can see these reviewers are deluded. The dumb thing in the interface so far is there's no good way to get back from the listing to the buzz.
5. OK, let's post something. If it can't find your location, like it can't find me, you can search for where you are at. It's limited right now to places in Google's database, so you can't Buzz from your apartment. Nobody's said anything about Ninth St. Espresso yet, so I'm going to right now. Make sure the blue location box in the bottom of your post - sometimes it doesn't follow through, which happened one of my earlier buzzes. Oh, an easy way to post is to use the voice search in the iPhone or Android Google app, starting your phrase with "post buzz." It works, to the extent that Google's able to normally understand you.
6. Now let's check out the Buzz Map, which shows me all of the Buzz going on around. The overlaid text on top looks terrible, but it works surprisingly smoothly, with responsive pinch-to-zoom. Buzzes, or whatever they're called, are the little chat bubbles you seeing hanging around me. Oh hey, Herrman again. And these other people. The easiest way to see what's going on, ironically, is to stick with the list view, which presents nearby Buzzes as a stream.
Overall, it's not very useful right now since not many people are using it, or at least saying anything worthwhile, but that'll change. Ease-of-use and the interface, especially in maps, when there's a million bubbles, needs to be massively improved, and at least on the iPhone it screams for a real app, not a web app - there's a few times it's made me wanna kill myself it was being so goddamn slow. One thing it could definitely use is a way to easily post photos from your phone. Also, could be annoying to get an email every time somebody comments on one of your buzzes.
Right now, mobile Buzz isn't an essential service. It's noise. That could change, just give it some time.
There's three components to mobile: A new mobile Google homepage with automatic geo-location and Buzz integration; a web app for Android phones and iPhone located here with full, incredible speech-to-text powers (especially with Android, which uses the built-in search widget); and a new version of Google Maps that tightly bundles location with Buzz.
In fact, location is the true killer feature here. While it lacks the gaming component of Foursquare, it's central to the mobile version of Buzz. Whenever you post buzz from your phone, it's (optionally) geo-tagged, and Buzz tries to figure out where you're at, offering a list of nearby locations it thinks you're at, and then embeds a map in your buzz showing your location. With nearby view, you can see what people are talking about around you, even people you're not following. From there, you can jump directly into a Google Places listing with reviews and comments. It's also another data layer in the new version of Maps, for you to see what's up nearby.
If there's anything it has as a one-up on Twitter, it's location. Because it's deep, and contextual, thanks to all of the services Google has, like Maps and Places.