To send out the manual dispatch email is easy, you just need to click the button in the order screen marked 'Send Shipment Confirmation Email'

Its best if you do a couple of things in the order screen first though:

1) Enter a ship date
2) Enter a shipping tracking number

3) Make sure the order status is not 'CLOSED' : dispatch notifications cant be sent to closed orders
4) Save the order before you click the send email button

5) click 'Send Shipment Confirmation Email'

note that if you don't have the ship date, the customer wont be able to return the item through the system if needed.
If you don't put a shipping reference then they will not be able to track their item.

Closing the order is a good practice because it removes it from the pending orders screen so that you don't send it out twice

1) Select 'CLOSED' from the status dropdown

2) click 'Save' to close the order