I am learning Japanese and I was wondering how to say something like this:
The [noun] that I can't [verb] is [verb].
The cat that I can't understand is talking.
Like in English, Japanese nouns can be modified by phrases. The sentence you gave could be broken into:
A cat is talking. ねこはしゃべっている。
I don't understand the cat. わたしはねこがわからない。
Combined, they yield:
The cat I don't understand is talking.
As you can see, one can simply prefix the noun with a descriptive phrase. It simply takes the place of an adjective.
Another example (from Tae Kim's Guide):
Who is person who watched movie last week?
The noun being modified is also not required to be the subject of the relative clause:
これは わたしのたべる おにぎり です。
This is the rice ball that I will eat.
Note that, as in this example, が is converted to の in relative clauses. That is a separate topic though.
Always keep in mind that Japanese is a head-final language and will put modifying clauses after the head.
For example, your sentence can be broken down as: the cat (that I can't understand) is talking. In Japanese this would be (私がわからない)猫は喋っている as seafood258 already stated. Japanese does not use words such as that or which, and will place the modifying clause immediately before what is being modified. Another example is (走っている人)が会社員でしょうか ->Is the man (that is running) is a businessman?