To add someone "to" Facebook or "on" Facebook

Adding someone on Facebook is generally accepted as a shorter way of saying "While on Facebook, I added someone to my friends list. The statement is meant to express what site you were on (visiting) when you added the new friend to your friend's list. Furthermore, when you "add someone on" a site, it's understood that you are adding the person "to your friend's list", which is why that part of the statement is not said explicitly.

Adding someone to Facebook implies you are creating a new account for her on the site.

The first sentence

It was the first time a girl asked me to add her on Facebook

is correct. She asked you to add her as a friend on the Facebook website:

It was the first time a girl asked me to add her [as a friend] on [the] Facebook [website].

The second sentence

It was the first time a girl asked me to add her to Facebook

is not absolutely wrong. If you happened to be the sole administrator of the Facebook website and had the authority to add and remove people, then the sentence would be correct:

It was the first time a girl asked me to add her to [the] Facebook [website].

In reality, however, this is not the case. You are both already on Facebook, you and the girl. That's the preposition that Facebook usually takes (also off in some cases). Thus, whether someone is sending a message, friending you/adding you as a friend, writing on your wall, etc., it's all on Facebook. Examples:

• I am being cyber-bullied on Facebook.
• I practically live on Facebook.
• I'm on Facebook every single day.
• Can you believe she sent a message on Facebook?!
• Can't you just get off Facebook for once?
• I need to get that creep off my Facebook [wall]!
• How many friends do you have on Facebook?
• Add me on Facebook now!

If you mean Facebook from facebook.com, you'll add someone on Facebook, since it is a website (or social network site).

I prefer on, but think either one would work.

What we're really saying is,

It was the first time a girl asked me to add her to my friends list on Facebook.

To and on are both part of the idea and we have two different approaches to making the friends list implicit.