downloaded here. The app already has 3,400+ ratings at the time of this writing, and a 4.3-star average rating; it's free for both iOS and Android.
For those who missed its explosion on iOS, the app was named the 2011 iPhone App of the Year by Apple. It currently has over 30 million users on iOS.
Once installed, you will be prompted to create an account (or login). You can then immediately "Find Friends" on Facebook, your contact list, or Twitter. You will also be prompted to "Follow" some suggested users (all of this, naturally, can be skipped and done later).
Then, start sharing.
You can use the Instagram camera to take images or use images already in your Gallery. Don't rely on the exact support documents on Instagram's website, at least for now. They appear to be iPhone-specific, as the instructions don't match up with the details of the app.
Once you select or take an image, there are a number of built-in Instagram custom filters and borders to choose from. You can also use Instagram's Lux feature which boosts contrasts in a manner similar to Camera+'s Clarity feature.
You can then upload the photo to your Instagram account and share it to Facebook, Twitter, Tumblr, and Foursquare; Flickr sharing is coming.
The app works with Android versions 2.2 and above that support OpenGL ES 2, and supports both front and back cameras.
There is probably a lot of pent-up demand among Android users. The Instagram iOS app has hit 30 million users after about a year and a half in the App Store, and about 180 million iPhones sold. Android has about 500 million activations, so a similar ratio would result in 83.3 million Android installs and over 100 million Instagram installations total.