Select a project or action and bring up the inspector (cmd-shift-I or Inspectors->Show Inspectors, or click the Inspector toolbar button). Enter/edit the dates as appropriate.
Another way is to turn on a column in the main window for the dates you want to enter. Bring up the View bar (cmd-shift-V or View->Show View Bar), and at the very far right you'll see a little gear atop the area where the window's scrollbar would be drawn if needed. That menu will offer a number of options for additional columns, including start and due dates. See "Customizing Columns" in the OmniFocus Help (cmd-?) for more details.
Also, be sure to check out the various tutorial videos available on the OmniFocus product page. There are some changes to the program that aren't reflected in the videos, but they are still worth watching.