Once you login, you will need to select the organisation unit, dataset and time period for which you wish to enter data. Once you have selected all of this, press the highlighted area to proceed to the data entry screen.
Data entry in the android app is very straight-forward. Data elements are listed along with their category combination option. Just select the field for which you want to enter data by clicking it and entering the correct data value. Values will be saved locally to your device. When you finish entering data, press "Save" and data will be saved to the server.