Before you can really can do anything useful with AvailApp, you have to at least set up a property with a couple of units. See Initial Setup
To create a new booking, first you need to find the unit (i.e. row) that you want to place the booking on. Then find the day (i.e. column) at which the guests arrive. Place your mouse pointer over the corresponding cell and press you left mouse button. Hold down the mouse button and move the mouse point to the right until you reach the day at which the guests leave. If the guests leave in the next month, just release the mouse pointer at the end of the month. After you release the mouse button, you can enter additional info and also adjust the dates.
Just click on any booking and a window will pop up. At the bottom of this window you will find a button to delete the booking.
First, make sure that the target unit is free during the whole booking period. Then, click on the booking you want to move and a window will pop up. At the bottom of this window you will find a botton to move the booking. After you click this button, you will be presented a drop down box of units that are free during the whole booking period. Select a unit for the list and save the booking.