When you receive payment for a job, all you need to do is click 'Mark Paid' for that job. This can be done on the schedule page, or anywhere you see the job you'd like to mark paid. In addition to the job being marked as paid, income for the same amount as the job cost will be created and linked to that job. If for some reason these 2 amounts will differ, you can either edit that income created, or add another income entry.
Tip: If you have received payment from a client that covers multiple jobs, navigate to the related account. Once there, you can see the jobs at the bottom of the page. You can them quickly click 'Mark Paid' for all the jobs that the payment covers. If the payment is meant to cover future mows, simply schedule out the necessary number of jobs by hitting 'Schedule Next', and then mark them as paid.