The Masonic Ring and the symbols on it is a probably the most recognizable emblem of the world's largest fraternity - The Freemasons.
Most commonly, the Masonic Ring has a symbol with a compass and square on the top. If the ring has a stone, it is typically either a blue spinel, synthetic ruby or black onyx. There are at least a couple of opinions as to whether the wearer of the Masonic Ring should wear the ring with the points of the compass either facing towards the wearer or away from them. The square is the symbol of all earthly, the compass is symbolic of heavenly perfection.
In a combined emblem:
 – The ends of the square point up as a symbol of man's aspirations toward God
 – The points of the compass point down to represent heavenly qualities coming down from God to earth.
It seems that the proper way to wear the Masonic Ring would be that in which its symbolism is best expressed - when the hand is held in its usual position the points of the compass are to the earth and away from the wearer's eyes. 
To wear the Masonic Ring, you must have achieved the degree of Master Mason.

Blue Lodge Masonic Ring - Freemason Band Ring 3rd degree - Silver and Gold
Handmade Masonic Band ring – Gold or Silver; Blue Lodge – 3rd ​degree; Square and Compass, G; Purity varieties - Gold or Sterling Silver; Customizing options – write a message; “Freemason Band Ring 3rd deg..
Blue Lodge Masonic Ring - G Square and Compass, Vintage - Silver and Gold
Handmade Vintage Masonic ring - Gold or Silver; Blue Lodge ring – 3rd Degree; Masonic Symbols – Square and Compass, Plumb and Trowel; Purity varieties - Gold or Silver; Customizing options – write a message; ..
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Handmade Masonic ring - Gold or Silver; Blue Lodge Freemason ring; Custom made; Hand engraved; Purity varieties - Gold or Silver; Customizing options – write a message; Watch Video Review below!; If yo..
Custom Blue Lodge ring - Masonic Skull ring, blue gemstone - Silver and Gold
Handmade Masonic ring - Gold or Silver; Masonic Lodge ring – Memento Mori Skull; Natural Diamond: 3 x 2mm; Natural Sapphire: 1 x 2mm; Hand engraved ring; Purity varieties - Gold or Silver; Customizing option..
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Handmade Masonic ring - Gold or Silver; Signet ring A.F. A.M. – Boaz & Jachin; Custom made ring; Hand engraved ring; Purity varieties - Gold or Silver; Customizing options – write a message; Watch Video R..
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Handmade Masonic ring - Gold or Silver; Masonic Lodge ring – Memento Mori Skull; Custom made ring; Hand engraved ring; Purity varieties - Gold or Silver; Customizing options – write a message; Entirely h..
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