Today's exercise is cribbed from the main Fantasy Worldbuilder page, which I wrote some time ago. I'll be pasting some of the text in, wholesale, but you can also go check it out for yourself.
Many people find this to be the most fun part of world-building. So many enjoy it, in fact, that there's an entire discipline called "conlangs." If you get started on this aspect of world-building and find it to be more fun than anything you've ever done before, you might want to look into conlangs, for creating constructed languages that didn't evolve organically, but instead were created artificially. Tolkein was a master of this, and created multiple languages for his Middle Earth setting. But then, Tolkein was a medievalist and a linguist, and creating languages was both a personal as well as professional interest.
If you're like me and just want to slide in a few new words because they sound "right," then do that. By all means, though, create a lexicon for your fantasy world's languages, though-- if the people of the S'nnari Desert tend to liquid sounds (lots of r's and l's), then any word with a "k" sound should be somewhat foreign to them, or have a particular impact when they say it (as in a curse word). People often say that German rarely sounds "nice," and it's somewhat true-- many hard sounds in the German language give it a much harsher "sound" to Romanized ears. The Star Trek producers were not stupid when they created the hard-sounding syllables of Klingon, either.
I can't suggest too many resources for the effects of sound, except that Mary Oliver's A Poetry Handbook has a chapter on sound that is amazing. It's all about the sounds of words-- the differences between vowels and different kinds of consonents, and what effects they have in poetry. Use this, or something like it-- Oliver actually took most of her information from an old primer on language she had lying around her house. Learn about how language sounds. I must also add: all the rules for sound are completely dependent on the native language of your listener. If you're writing in another language, your rules for what sounds "hard" or "soft" will be completely different.
You can also feel perfectly justified stealing liberally from Earth worlds and languages; many authors do this to great success.
Most of the time, you'll be writing in your native tongue, and so you'll have automatically "translated" whatever your characters are doing into the language you're writing in. You need to know what your characters' language sounds like only for those words that you want to add in, to give an exotic flair to your world. In general, these will fall into three categories: people, places, and things. Verbs, being more abstract, should not be presented in your made-up language unless absolutely necessary. Even then, try to make those verbs sound as close to your own language as possible.
One other resource that can be valuable in your search for good names: Baby name books. Both for parents and, now, more generic ones for writers. I have two naming books that I find helpful-- one lists the names by cultural association as well as first/last and male/female names. The other one is a book specifically geared towards naming fantasy characters, and is published by Writer's Digest Books.
Listen to how different syllables sound to you. Do they excite you? Do you associate a particular sound with an emotion or place or memory? Write down some generic preferences for your languages-- "I want the language spoken by the elves to sound like water, and the language spoken by the dwarves to sound like gravel rubbing together" and then go listen to what those things sound like. Write down the syllables you hear when you run a faucet or sit by a stream, for instance. Those sounds will be your "root" syllables when making up your names for places and people and things.
If you want language to play a strong role in setting the mood of your story, visit the naming exercises from the page mentioned above, and sort out some of your names for your people, places, and things. Note that, in doing this, you will likely get a firmer grip on your character's background, as well as need to pull out your map to now fill in the names of some of your key landmarks and settlements. This will probably take an addition 15-30 minutes more.