How is the ring able to perform more than one operation at a time? Has an operating manual ever appeared?
Depending on the skill and willpower of the wearer, it can do almost anything.
The rings use pure energy supplied by a Power Battery, which in most cases takes the form of bright green light. This energy is the green light of willpower of the Emotional Electromagnetic Spectrum. A green lantern ring has the ability to affect and use fundamental forces of the known universe, including electromagnetic energies such as gravity, radiation, heat, light, and powerful blasts of concussive force. The ring can also create fields of force formed from an unknown energy that is bound by the users' will. The limitations of such use are the skill, knowledge and imagination of the user. -DC Wikia
Hence, it is possible to do any number of simultaneous actions, as long as the ring is powered and the user is skilled enough.