She had a diamond ring on the ring finger of her left hand.

Literal

She [topic-は] left-hand [genitive-の] medicine-finger [on-に] diamond [genitive-の] ring [object-を] was-wearing.

The Japanese name for the ring finger is 薬指 (kusuriyubi, 'medicine finger') — said to come from the old practice of using this finger to apply medicine, since it touches little else and was considered the cleanest. Each finger has its own name in Japanese: 親指 (thumb, 'parent finger'), 人差し指 (index, 'person-pointing finger'), 中指 (middle), 薬指 (ring), 小指 (little). はめる is the specific verb for putting on rings or fitted accessories — distinct from 着る (wear on torso), 履く (wear on feet), かぶる (wear on head). The progressive ~ていた gives the resulting state: she had it on, not the act of putting it on. ダイヤ is a clipped form of ダイヤモンド ('diamond,' English loanword).