To book your vehicle just shift over to the book tab of the app. You will then need to pick the Private Fleet you are associated with ('Mevo Private Fleet' is used here as an example). You can then select your preferred date and time for the booking as shown below.
Once your date and time are chosen you will be shown the duration of your booking, following which you will need to click 'Search' and then choose the vehicle type you wish to book. Following this you can confirm your booking as shown below. Once the booking is successfully confirmed, it will appear in your Book tab as an upcoming trip.
Below is a sequence of the whole booking procedure.