Unfortunately, Google Drive for iOS is only a viewer and a very basic document manager. It will display the documents without any problems and would even let you download them if you expect to not have a network connection. However, it won’t be possible to edit them for now.
Of course, this is a bit of a disappointment, but it is fair to assume that editing support will come eventually. The question is “when?”. In the meantime, Google can gather data and ramp up its infrastructure for the new incoming traffic. The thing that I miss the most: being able to display the last modified files like the web version does.
On computers, Google made offline editing available for the Chrome browser. Now, documents can reside locally for a period of time, and will be synched back whenever network access is available again. At the moment, only the text documents can be edited offline, but Google says that support for presentations and spreadsheets is coming. To enable offline editing, go the Google Drive app settings.