Take the word fellowship, for example. You'd think that since Elrond actually calls Frodo, Gandalf, Boromir, et al., "The Fellowship of the Ring" then there's probably a word for it in elvish. Nope. Turns out it's only a movie thing anyway. None of the characters in the books ever refers to the fellowship as such. So you start going through vocabulary lists looking for words that can be substituted, say society or company.
This isn't particularly easy. There are plenty of Sindarin dictionaries online, of wildly varying usefulness, each with its own set of translations. Oh, they generally match up, except when they don't at all. (It's even worse when you read different takes on Sindarin grammar.) The closest match I found using a dictionary was gweth, which means troop. But it's kind of an ugly looking word, so I kept looking around.
There's the website called Fellowship of Word-Smiths, who are a good source for folks interested in elvish liquistics. They translate their own name as Gwaith-i-Phethdain. Among other things, gwaith is the plural of gweth, so it means troops, which seems like overkill for a fellowship. Gwaith also sometimes means people or folk or a region. It's a very all-purpose word. Either that or Tolkein's spelling wasn't the best when it came to elvish. That said, it's a little prettier to me than gweth.
Jackson and company created a lot of elvish dialogue for the movie, along with coining some vocabulary, and it turns out Legolas refers to the Fellowship when the meet up with Haldir:
Legolas: Govannas vîn gwennen le, Haldir o Lórien.
Subtitle: Our fellowship stands in your debt, Haldir of Lórien. [link]
Except govannas comes from the root govad, which means meet. So govannas would literally mean group that meets, which sounds more like a council than a fellowship to me. I could see the Council of Elrond translated as Govannas Elrond, for example. However, some googling shows that govannas seems to have become the preferred word for fellowship among those who set up websites devoted to fellowships of various sorts, if not those who compile dictionaries. Elvish linguistic relativism in action. Still, I like it better than gweth or gwaith. I could always use gwaith as part of specific names, while using govannas as the more general term. Or not. I keep having to remind myself that when you're doing fiction you can make stuff up. This isn't going to be Tolkein fanfic, so authenticity is a plus, but not critical.
Near as I can tell, the plural of govannas would be gevennais. I am such a sad and lonely man. (Im benn annaer ah erethren.)