Networking

I have recently applied for an intern position to a company and recently I found the hiring person's lindken profile and connected with her. Now I really want to send her a message maybe introducing myself or something of that sort, something that puts me out in the front of the other applicants, but I suck at it and I really don't know what to say.

Please help me!

PS this is a rolling position and I am applying as a bachelor student who is still studying. Thanks!