1. The pseudo-philological school. These are those such as MAR Barker and JRR Tolkien, for whom constructing coherent languages is an enjoyable hobby and actually probably the main attraction for them in the genre of fantasy. This is by far the smallest.
2. The instrumentalist school. This is the use of language and linguistics to achieve fictional goals. One example is China Mieville's Embassytown, in which an alien language which requires being able to say two things at once and living people to act out similes is a sort of plot device for weird stuff to happen. Another is the Star Trek: TNG episode "Darmok", in which an alien race is discovered who can only communicate using metaphor - again as an interesting plot point.
3. The aesthetic school. This is the largest, and comprises the great majority of fantasy writers, who simply make up words as and when they need to because they sound good. An example of this is George RR Martin, who invented a "Dothraki" language in some notional sense (the language exists in the setting) but who just makes up Dothraki words when he needs them; they sound sort of suitable from an English-speaker's perspective for a culture of steppe-travelling nomads. Most fantasy languages are like this, and are typically conceptualised in quite a lazy way, so if there is a culture of people who live in small mutually antagonistic city-states the languages they speak will sound vaguely Italian; if there is a culture of people who live in hot exotic climes their languages will have weird clicks and apostrophes everywhere; if there is a culture of people who live in the desert their language will sound harsh and guttural; and if there is a culture of people who live somewhere cold their language will have lots of umlauts and feel vaguely Nordic.
I've always been fascinated by languages, especially the rare ones. Different languages really are different ways of looking at the world. Perhaps the best and most striking example of this I know of is that the Japanese word for 'blue', aoi, also often is used to mean what an English person would call 'green'. I was amazed when I first moved to Japan and started learning Japanese, and realised that people actually referred to a grass lawn or a 'go' sign on a traffic light as being blue. This rather trivial example illustrates the depths of difference which exist from culture to culture, and what a tragedy it is when one of these unique ways of looking at the world disappears.
The variety of human languages is also pretty astounding. Listen to the sounds of these three people, speaking Ainu, O'odham and Scottish Gaelic respectively. Pay particular attention to the noises they are making. The variety is impressive, and what you will notice is the absolute poverty of imagination that there is in the English-speaking literary world when it comes to thinking about what potential fantasy languages might sound like.
Yet it is also perhaps worth pointing out that there may be a fourth school of thought regarding languages which is even less well-acknowledged - it's not so much implicit as subconscious. And it's this: if, like Tolkien, you conceive of fantasy as being a kind of "legendarium", then it may be entirely appropriate to approach the construction of fantasy languages and words as being an exercise in communicating meaning rather than in being realistic. A good example of this is the use of words in Mythago Wood; I don't believe for a second that the words used in that book are at all accurate as examples of old Brythonic or whatever, but the word urscumug has a great ring to it as a word for a kind of hellish guardian monster of the forest. Similarly, I would say that the word orc has a certain feel to it for English speakers which is suggestive of what the word "orc" represents. Fantasy languages, in other words, have a role to play in creating a mood for their audience that is representative of what that audience understands "fantasy" to be.
It is suitable and appropriate, then, to think of fantasy words as having to communicate mood to the readership rather than making sense from a linguistic point of view. Yet the observation that there is a poverty of imagination there also holds true: if you want to be interesting and different, you could do a lot worse than listen to how people in other parts of the world (especially its more obscure corners) actually communicate with each other.