One good way of showing different cultures in fantasy (or SF) writing is to develop different languages for them: Tolkien took this to grand heights of course, but general practice now seems to be to sprinkle in a few ‘foreign’ words to prove the ‘other’ nature of the character or culture.
This can be done well: I mentioned in my post about CJ Cherryh how much I admire her use of made-up words to genuinely express concepts that can’t be translated into English (or whatever language is representing the dominant language of the fantasy world). The most obvious example of this comes from her excellent Foreigner series, where the human translator’s job is made difficult by the concept of man’chi which cannot really be translated into English in any easy way.
I also mention in that post that I dislike the use of made-up words to just straight-out replace words we already have. If it’s tea, call it tea; don’t call it chai just to sound clever (as I said in that other post, if all the other words were translated, why wasn’t that one?). I do have to admit I did a little of this in After the Dragon – using kafa for something that might as well be coffee, but I was trying to hint that the stuff was new to the society, in the same way coffee was once new and foreign to Europe; it’s a reminder that there’s more to the world than just the three little nations my characters pass through.
It’s up to the author how much they want to get into this: where the book is focussed on just one culture/society, it’s hard for made-up words to be anything other than fake swap-outs of the sort I find unnecessary and distracting…it’s like when authors want to remind readers that their characters are actually speaking French so they whack in a French word occasionally – which of course destroys the illusion that they’re really speaking French translated to English because otherwise that lone French word would have been translated too…
Where there’s more than one culture/society, however, foreign words can be a handy tool to show that different characters come from different cultures; this is how I mostly used the made-up words in After the Dragon where there’s two dominant cultures splintered into at least two societies each. It can be more than a handy dialogue marker, of course – it can be a device to show that the characters think differently to each other (and us) too. For example, the Atevi of Cheryh’s Foreigner series have no concept of love as such, and therefore no words for that or friendship and so on.
In my own current fiction-writing, the difference between the corniche culture and the valley systems culture has become clearer and clearer, and I will represent that in their language; in particular, there’s no nasty words for women (you know the list: slut’s pretty high on it) in the valley systems Dialects, where their god is a cheerful little guy who wants everyone to just enjoy life as much as they can (Sex! And lots of it!).
It’s intuitive to think that if a culture does not have a word for something, they don’t or can’t think about it, and it’s my natural inclination when working out a sub-culture’s language. However, it’s not necessary true: the works of linguist Steven Pinker are good for examining this. For example, he mentions briefly in this interview his view that in fact language does not drive thought as much as we assume; the obvious example being that babies are perfectly capable of thinking before they learn to speak. Being able to think abstractly about something and being able to express it in words are two different things.
Therefore, my concern with language is often not to try to work out good made-up words to use or which words to omit, but instead to make sure the language’s metaphors match up with the society properly. In the corniche culture, for example, their stern god is the Starving God: every sin takes a crumb from his mouth, and since everything’s a sin, He never gets to eat. Therefore, a lot of the imagery and metaphors centre around eating, vomiting, or going hungry. Something like ‘that cuts no ice with me!’ becomes ‘that won’t feed my hungry mouth’.
If you do want foreign-sounding words, there’s a number of options: random word generators (plenty online, just do a search), existing foreign languages (I used modified Japanese in After the Dragon), archaic English words (swiving, for example, used in The Last Witchfinder), combining word roots to create plausible sounding new words and so on.
The importance lies not so much how you do, but the thought you put into it: don’t do it just because you can. Know why you’re doing it.

Excellent thoughts. Ultimately, your last sentence should be the guiding light for authors in whatever stage they find themselves: be deliberate in all you do. Have a reason for the things you set up within your world. Readers are sophisticated things, and they know when something is a sham.
It should be the first rule of writing: treat your reader with respect. Trust they will get your themes without being beat over the head with them. And trust they will pick up on what is not authentic in your writing, too.