In both examples -the artist in your case -music producer would do all that you can to work with independent artist who might have a situation developing and/or a strong Internet, street, club or radio buzz.
If you have heat (hit music) it makes things a lot easier for you. The other thing is having a pleasing personality. This doesn't mean that you have to kiss *ss per se, but it does mean that people have to believe they can put you in the studio with Mariah, Whitney and Janet, etc. and you'll perform as a music business professional.
Many people have gotten placements by working in a particular recording studio and networking while there. There's no specific way, but then again there is. There's no specific way because it's not like educating yourself to become a C.P.A. or attorney where the process is clearly laid out. However, it's a specific way because of what was mentioned earlier about having hit music, a pleasing personality and building your own buzz. Through these efforts you'll see results, as long as you don't get out the game (music business).
Always have a written music business contract with whoever you're working with especially as it relates to artist/manager, music producer/manager and songwriter/manager relationships. Having written written music business contracts keeps everyone from collecting amnesia when royalty checks start rolling in.
For additional details download either the Atlanta Music Industry Connection or Los Angeles Music Industry Connection Ebooks.