If you just would like to go to a ward there aren't any requirements at all. You just need to show up and then have your records transferred and they'll be happy to take you!
Also, I know you asked about language-based wards specifically, but BYU also has foreign language housing as well and if it's something you might be interested in I would recommend giving it a look. If not, you can stop reading right now because I answered your initial question and the rest of this talks about foreign language housing.
I am currently living in foreign language housing right now and I love the ward. It is seriously the best ward ever and I love having group dinners. It's an amazing opportunity that I think everyone should do if they can. Here is the link for the application so go fill it out right now! Your chances of getting in are better the sooner you apply so get to it!
There are some qualifications. The three main ones are: you have to take a language class every semester you're there (They offer 2 credit conversation classes that are just 1 hour a week), you have to commit to going to group dinners, and you have to have some basic language skills. The official language requirements according to the FLSR (Foreign Language Student Residence) website are: "Completion of the following prerequisites is recommended: 102 for ASL, Arabic, German, Portuguese, Russian, and Spanish; 201 for Chinese and French; and 202 for Arabic, Japanese and Korean. Faculty Coordinators will discuss course requirements with returned missionaries... Please call (801) 422-3765 or e-mail us at firstname.lastname@example.org if you have any questions."
Basically, you will apply and you will be interviewed by the language coordinator for the house you're applying to. How strict they are about the requirements depends on the house. I know that the Portuguese coordinator is pretty chill as long as you have some skills and a desire to learn. I know that other languages are very strict. It just depends on the language. Hope this helps!