It is very easy to create a 1 to 1 cipher which will sound linguistically plausible. I've done this several times, for many different languages. It's also easy enough to break that, given enough text, the players could figure it out.
Effectively, what you do is map vowels to other vowels, and consonants to other consonants, and drop
Y (and likely also
Q). Another way to do this is to map sounds to sounds; this turns out much more realistically than alphabetic substitutions, but it's much harder for players to break. I'll give an (admittedly poor) example of the first one here:
A -> E
E -> O
I -> A
O -> U
U -> I
Then, map consonants to other consonants in a realistic, but creative way. The letters you map will determine how the "language" sounds. Take a look at this chart when creating the language; if you want hard sounds, for instance, you might map
Thus, create the table, and remember to skip the letter
Y. You may also want to drop the letters
C's sounds are covered by both
Q's sound is covered by
B -> L
C -> H
D -> K
F -> J
G -> X
H -> F
J -> N
K -> M
L -> D
M -> V
N -> W
P -> C
Q -> T
R -> Z
S -> B
T -> S
V -> P
W -> Q
X -> G
Z -> R
You're effectively creating a cryptogram puzzle at this point. So, let's take a phrase (You'll note that I interpreted
Hello, my name is Richard.
Foddu, va wevo ab Zahfezk.
Obviously, you're going to encounter some conflicts. Simply put, Zahfezk really doesn't roll off the tongue. You may want to stick with that, though. It's okay to tweak it a bit at this point - but remember, if you want them to figure it out, don't change too much.
Note that this cipher probably won't work for most things, since I didn't give it all that much thought when creating it, and I didn't drop
Now, it's very easy to create a symbol set for this. Depending on how in-depth you want to go, and how hard you want your players to work, you can either do this with another 1 to 1 cipher, or you can create a phonetic transcription. Either way, it's a simple as creating a new symbology, either for sounds, or for characters.
Note: Never translate names directly. They will not come out right, I guarantee.
Playing around with phonemes to specifically customize your language
If you do choose to create a phonetically structured language, you can much more easily create a specific custom language. Feel free to play around with digraphs and trigraphs; your language no longer needs to map perfectly both ways. For instance, if you wanted a more snake-like language, you might map
SS; if you wanted a Nordic-sounding language, you might map
SVE (as in Sverdya).
You can even mess around with vowels, though be aware that you'll screw up a lot or words if you do this. A draconic language may map
KOL (as in D'kolbochya, the Great Palace of Dragons).
Presenting the language puzzle
All languages evolve over time. In order to keep things interesting, you're going to need to keep making symbols. The core structure of the language is already there. While we don't see it so much with English, it's fully possible for a language to accrue more symbols.
Start with complex symbols. Make them intricate and difficult to copy. (Optional: don't let your players keep notes on the language; I wouldn't do it, but it would alleviate the problem.) Then, as you give them more and more texts, slowly change out the symbols for simpler, cleaner ones. This has the added benefit of giving the language an evolution path; it becomes much more realistic when the language changes.
Lastly don't let your puzzles rely on one immensely complex aspect, like a written ancient language. If your players only need to break the cipher to recover the ancient crystal key, then they are going to smash your language to pieces. Instead, base puzzles on multiple aspects; leave language-deciphering as a pastime for the players. You don't want to alienate them with a frustrating puzzle. Your group may become dependent upon one person to decipher the text, if they break it. Additionally, a player with Comprehend Languages could break the puzzle entirely, without effort.
Use language puzzles in moderation.