First understand that the general idea is that you open MileBug right when you get in the car to go somewhere. You add a trip, enter the data including the starting odometer reading. Then you close it up and drive to your destination. When you arrive, open MileBug and it will automatically take you to the incomplete trip where you now simply enter the ending odometer reading and hit Save. Voila! Now it's in your Trip List.
For the simplest case, focus only on the Trips tab. Don't worry about the others right now. On the top right, there's a "+" button. Simply tap that to add a new trip. You'll see a new screen slide on with different fields for information about the new trip you're about to take. Simply tap on each one to either choose or enter the data for that field. For fields like Business, Destination, Vehicle, etc. you'll be adding a new one to the system by tapping "Add Preset" at the top of the screen that appears when you select Business or one of the others. Simply add the new one, and it will now appear in your set of Businesses, Vehicles, etc. that you can choose from for this trip and all future trips.
If you want to customize a few things, you can do this in the Presets tab. There you can choose among different settings, as well add/edit/move/delete your set of Businesses, Vehicles, Expense Categories, etc. Keep in mind that each business has it's own set of Destinations and Purposes.