Answer
You can add employees into a pay run they're missing from in the Pays tab, by clicking on Create Pays from the particular pay run they're missing from, selecting the employee/s to add, then clicking Create. By having Create Full Pay? ticked at the bottom of the Create Pays screen, the program will use the hours and rate of pay set in Employees >> Pay Settings >> Pay Rates to pre-fill the pay for you; rest assured, you can still edit these pays like normal using the Edit Pays buttons on the main Pays tab.
If you have added a new employee and you're not able to find them on the Pays tab or add them using Create Pays, it is most likely that you have set an incorrect Start Date for the employee when adding them to the program. You can fix this by going to Employees >> Details >> Employment Dates and updating their Start Date to the correct date, then go back into Pays and the pay run you're after, and said employee should automatically now be in the list of people to pay.