There are other names in addition to these, but the primary ones are;
親指 (おやゆび oya-yubi) "Parent finger"
人差し指 (ひとさしゆび (hito-sashi-yubi) "Person-indicate Finger"
中指 (なかゆび (naka-yubi) "Middle Finger"
薬指 (くすりゆび (kusuri-yubi) "Medicine Finger"
小指 (こゆび koyubi) "Little Finger"
All of these are intuitive except for the "Medicine Finger," whose name originates in the Heian period when it was used-- as it is weaker and thus gentler-- to apply medicine.
I don't know that that's enough to constitute a full lesson, but I thought it was an interesting little cultural factoid.
High time to finish what I've started. || Anki vocabulary drive: 5,000/10k. Restart coming soon. || Dig my Road to Katakana
tutorial on the App store.