I'll start.

Since she said something that i think was "I will see my home again"

My first guess is that she is from the same city as fizz and go some place then returned later like fizz to see everything gone. She then hears that there was a survivor then join the league. ( Although this may not be true but the despair in her voice imply that her home was lost through violent actions)

Or she is a mermaid living with others of her kind when she is pulled away by a summoner.

Or Nautilus met her in his journey home and sort of kind of "took" her with him :P

Leave your ideas below

Nami! Nami!
Nami was a maid!
I mean, she was a Mermaid!
Or maybe she was just a Mer...
But she was still Nami!!!!!
Nami!

I have passion for water

She joins a crew of pirates and then gets separated on a Giant archipelago made out of Mangroves, It's been 2 years since her separation and she wants to go back "home" to her crew, so she joins the league to have a higher chance of finding them.

Nami lived in the sea, but she heard tales of a fish named Fizz who joined something called, "The League of Legends." She then spontaneously grew an uncontrollable urge to kill Fizz. She then joined the League with her newfound purpose.

The end.

Heh heh..

No no no. It's quite obvious, really.

She dreamed of one day becoming a human. After saving a man from a shipwreck, she fell madly in love with him and vowed to one day be a part of his world, and thus joined the League of Legends.

nami wun 2 be walk on 2 fet but dad say no n she go 2 oktapus n tern in2 human wif 2 fet den evil oktopus cas evil spel on her den her huzben erick halp her kil evil oktapus n den she hapy.

Nautilus little sister

Well guys...I'd hate to burst your bubble.

But I bet Nami is what happens when Jax uses the Super Rod instead of an Old Rod.