How to approach a guy I don't know but like?

Basically, I just started working at my local hospital doing some admin work. I went to the canteen/cafeteria alone for my lunch break on Monday and this really cute guy sat at a table close to me. I was making some notes at the time and I kept on catching him looking at me. Whenever I caught him looking and we shared eye contact for a second, he'd quickly look away and go on his phone. This same thing happened yesterday except I smiled at him. I also saw him later in the day while running some errands and I disocvered he works in the HR department, and he glanced at me some more. Today however, I got really close to approaching him but I chickened out last minute.

At 19, I'm one of the youngest people working at the hospital and I think he's of a similar age . Also, I feel like I know him from somewhere else, maybe school or college?

Either way, I really want to try and approach him and possibly strike up a conversation. But the problem is that while I'm confident, I'm very shy and I get nervous talking to new people. I've asked some of my girlfriends about this and they've told me to sit at the same table as him, but since there's always tables free I feel that would be awkward. I just want to approach him in a way that doesn't seem too forward or creepy, and hopefully this will initiate a conversation and one flirting so we can get to know each other better.

Please help me out!

- Louise