Here's the answer:
“よろしくおねがいします”
(yoroshiku onegaishimasu)
Watch a real native speaker say it:
Here's how it sounds in a textbook:
You could also say:
- よろしく
- よろしくお願いします
Fun fact: the hundreds of thousands of people learning Japanese with Memrise get this phrase correct 89.23% of the time!