Desktop
I first downloaded the desktop app as a free trial. Then enabled sync via Dropbox. Then I downloaded the Chrome extension so it could auto-fill everything in Chrome on desktop.
iOS/iPhone
Then I downloaded the iOS app on my iPhone, than I followed these instructions to add 1Password functionality to my iOS Safari.
Previously
Previously I had been using KeePassX on desktop (no iOS functionality that I’m aware of), but I was a bit too afraid to save my encrypted database to my shared Dropbox folder. Though if I was willing to sacrifice the iOS functionality and the Chrome extension, I’d probably go with the KeePassX + Dropbox solution.