1. Be able to translate a song or aria from the original language into your own language. This is step 1 for the process of learning vocal music of any style and genre. If you know what the song is about on a detailed level, you will already be able to play or sing it at a higher level.
2. Write the translation above the vocal line in the score. This way, you can learn the meaning of the words and get them into your bones through osmosis by having them written in such an obvious place.
3. Learn the International Phonetic Alphabet. There isn't always a one-to-one correspondence between the sounds of a language and its IPA symbol, but knowledge of IPA does provide a common ground that allows the sounds of language to be talked about objectively.
4. Learn the basics of lyric diction for the languages central to the repertoire. Italian, German, French, and English, are the languages most encountered. Other languages encountered include Russian, Latin, Spanish, and Czech.
5. Learn the basics of the langages central to the repertoire. Nothing beats knowing the building blocks of how a language works and getting a good start on the road to fluency.
6. Become fluent in the languages central to the repertoire. Not every collaborative pianist will spend time achieving this difficult and time-consuming skill. The best way: spend some time in a country where the language is spoken either as a visitor, student or professional. Being able to speak and talk about a language with the experience of fluency will repay many times over the time spent in acquiring it.
7. Be able to talk about poetry and poetics. Knowledge of how poetic language is constructed from the ground up can greatly help the transition from accompanist to vocal coach. One of the things that singers need from coaches is a way of understanding the techniques of poetic languagte as a route to motivating the performance. I recommend Mary Kinzie's excellent A Poet's Guide to Poetry as one of the best ways of learning the tools of the poetic trade.
8. Be able to talk about librettos. Learn not just the text of the aria or scene, but the text of the entire work. Libretto-writing is an art closely related to playwriting, but different in many significant ways.
9. Learn song cycles in their entirety. The time spent will more than reward you in the knowledge gained from such a process.
10. Learn operas in their entirety. Ditto.