Putting music from itunes to iPhone?

I use one computer for my songs in iTunes. I have an iPod Nano (3rd gen) and it's already synced to the computer I use (which is the one I'm using right now to ask this question).
I got the iPhone 5 pretty recently (Sept 26th), and I want to put the songs that I have in my iPod Nano onto my iPhone 5 for those moments when I don't wanna bring both with me. How would I do this through iTunes?
BOTH of these devices use my same apple account, so how would that affect the iTunes thing if I just plugged in my iPhone? I'm just worried that if I just plug my iPhone in that it'll erase the songs that were synced to my nano.
I'm really confused because I don't want any of my songs to get deleted. Long story short: I want the same songs I have on my nano to go in my iPhone as well (without accidentally deleting anything or messing anything up permanently).
I'm not super techy, so please be as specific as possible! Oh and I use Windows (I think it's Vista?)

Added (1). @MrMoustache person, I don't really understand what you mean by "taking both"? And when you say that it'll erase the iPhone 5 stuff, did you mean that it would only replace the music on it (if there's any)?
Oh and I forgot to mention that my iPhone 5 has NO music on it whatsoever, it's a clean slate basically except for some apps and stuff.

If you sync your iPhone to your computer synced to your iPod nano, you'll loose everything on the iPhone, and it will be replaced with what's on the iPod nano. I'd just suggest taking both