"Hey there, I saw your company was hiring and I wanted to reach out about X role. Feel free to reach back out if you feel there might be a good fit or if you have time to talk more about roles at Y."
I guess he meant it in a broad term and it's up to you to get creative. Now that I think about it, you can start by complimenting the resume for the employee you are interested in, and ask how he/she got there. Generally, if they are open to helping they’ll drive the discussion forward. Needless to say, if your first message/email is "please recommend me" it won't work. Personally, I always get back to first principles: Provide value first before asking something back.
"Hey there, I saw your company was hiring and I wanted to reach out about X role. Feel free to reach back out if you feel there might be a good fit or if you have time to talk more about roles at Y."