Using a Green Lantern ring is requires two things: great willpower and the ability to overcome great fear. Willpower is the 'emotion' (using the term loosely) that powers the Green Light of the emotional spectrum, from which the rings draw their power. The wielder's willpower is channeled through the ring and made manifest. This obviously requires you to have significant willpower: more will translates into a more powerful construct.
The second part, overcoming great fear, is heavily implied to be something the Guardians built into the rings. In the previous continuity (before New52) Parallax, the Incarnation of the Yellow Light of Fear, had been stored in the Green Central Power Battery, giving the green rings a weakness to yellow. This weakness also meant that a Green Lantern, if afraid, would be vulnerable to Parallax. Therefore, the Guardians built in a test - each time you use the ring, you must overcome your greatest fear.
Batman tried Jordan's ring once. It ended badly for him:
That said, so long as you have a sufficiency of the relevant emotion (Rage, Avarice, Fear, Will, Hope, Compassion, Love) and a tool which channels that power (* Lantern rings or the Indigo tribe's staffs) you can use the tool to create constructs. Any given channeling tool
could have other restrictions built in.
The rings, driven by the Guardians directives, seek out people who have the capability to overcome great fear because the Guardians know that doing so requires great willpower. That, in addition to proximity, is what drives the selection process for Green Lantern rings.