Everyone in my neck of the woods pronounces it too-na.
Tuner or chewna, both sound the same 
Or Tsuna lol. They are basically the same just spelt different.
You can tune a piano but you can’t tune a fish.
Choona
Too-nah inna cahn, a-yuh!
“It’s not a too-na’ (Arnie)
I fear I might just be a poshly spoken Brit :o
http://www.macmillandictionary.com/pronunciation/british/tuna
Tuna, with a U.
Ah i didn’t realise the poster is kiwi. Maybe we can also ask how to pronounce fish and chips? lol 
Chicken Of The Sea
Nothing like a good too-na steak seared on the outside, rare on the inside!
a Chicken of the sea
In Hawiian it’s “humahumanupanupaapua’a” 
Phil
Tune-Ahh
John.
Wow, I don’t care how you pronounce it, there’s a lot of money in that net!
Like this.
Thanks to those that have voted and/or commented so far! There are some interesting and amusing results!
I wont mention anything about "feesh and cheeps" either! 
The inspiration behind this topic was that I had some canned (tinned) tuna that I didn't really want nor need. So I took the tuna to give to my next door neighbor, an elderly lady. By chance one of the ladys' daughters happened to be visiting. So when I mentioned that I had some "too-na" to give away, the elderly lady and her daughter started talking about "tyou-na" this, "tyou na" that, and "tyou-na" the other.
So I was wondering about the pronunciation of the word tuna. Hence this topic was created.
As suspected, the pronunciation of tuna as "too-na" (or "too-nah") is more american (and for countries influenced by North America). And the pronunciation of tuna as "tyou-na" (or "chew-na", or "choo-na") is predominantly British (and for countries heavily influenced by British culture such as Australia and New Zealand).
I prefer "too-na", as it sounds right to me. "Tyou-na" doesn't sound right.
As you spell it.