95% of my knowledge regarding Lord of the Rings comes from reading Science Fiction & Fantasy StackExchange, so I apologize for my ignorance.
In many questions, I often see a powerful elf (Glorfindel, Elrond, Galadriel, etc.) described as an "elf-lord." At first I thought this was a general compliment/deference to their power, but then I noticed that it is capitalized in nearly all cases. It sounds awesome, but what exactly does this mean? How does one gain the title?
In the Tolkien universe the title "Lord" when applied to an elf can mean a leader or king, or alternatively member of a noble house.
Examples are:
It has the very same meaning as for humans: Lord and Ladies are nobility and you gain the title through inheritance. All of the different elven races have their royalty and nobles. The elves in your question are all of Noldor, who also traditionally have a High King,
Noldor royalty in Middle-Earth is divided in three houses after the three sons of Finwe, the first High King. There is the House of Feanor, House of Fingolfin and House of Finarfin.
At the time of LotR, Noldor are dwindling and there seems to be a general reluctance to pick up the titles King or Queen. The last High King of Noldor was Gil-Galad, who died at the end of the Second Age, in the battle against Sauron where Isildur cut off the ring from Sauron's hand.
Elrond is the one with the claim to the title, being the highest ranked alive member of the House of Fingolfin. He is technically a King but doesn't use that title. So the honorary used for him is Lord, even though he is actually royalty.
Glorfindel is a Lord, a nobleman, who was the head of the House of the Golden Flower in the first age, a nobleman serving Elrond's great grandfather and once High King, Turgon. Turgon ruled the city of Gondolin which was destroyed in the wars of the First Age, and with it Glorfindel's House, though he remains nobility.
Galadriel is the highest ranked member of the House of Finarfin in Middle-Earth. Her father is actually still alive in Valinor, making her a Princess formally, though she never took up any titles. Same deal as with Elrond, since she didn't take up any titles the honorary used to address her is Lady.
Elf Lord is a title bestowed on an Elf that is given an Elven Ring of Power. With the single exception of Gandalf.
"And here in Rivendell there live still some of his chief foes: the Elven-wise, lords of the Eldar from beyond the furthest seas. They do not fear the Ringwraiths, for those who have dwelt in the Blessed Realm live at once in both worlds, and against both the Seen and the Unseen they have great power."