Late to the party, as usual

But hopefully I can be of some help here.
We can start with the origin of the name, a little etymology is always fun!
Husqvarna is an older spelling of the town/area name Huskvarna. We used to love Q in words and names here, but not so common these days and mostly replaced with a K.
The name consists of two words put together, 'hus' and 'kvarn', with a dialectal A added at the end - Hus-kvarn-a.
Hus means house, and kvarn means mill, so put together it would be Housemill in english.
And the origin of the name can be found in an old mill that was located next to a river called 'Husån' (later renamed 'Huskvarnaån). The locals called the mill 'Huskvarnen' (the house-mill), since it was a mill located by 'Hus-ån' (the house-river).
This was a few years back, the industries that in 1867 became Husqvarna AB were built near Husån in 1689.
The mill itself was even older, but I can't find any information about when it was built. What is known is that there was a castle called 'Rumlaborg' built 1366 (in ruins around 1500), and before that a bishops house built sometime late 1200- early 1300. I'm guessing the mill was built in connection to one of these two, but take my guess with a big grain of salt
Soooo... on to the pronounciation! One thing I notice in the replies above is that you tend to put the 'k' ('q') in the first syllable, Huusk or Hoosk, but the first syllable is just 'Hus'. Perhaps this comes from the english nickname Husky (in Sweden we usually shorten the name to Qvarna when talking about the brand, not Husky).
The 'u' is a long soft vowel, wikipedia suggests like in the word 'mood'. Not quite sure I totally agree on that, but can't come up with a better example at the moment
The 's' is a regular s like in the word 'silent'.
Next part, 'qvarna'. If you look at the more modern spelling 'kvarna' it might be easier to understand the pronounciation.
The 'q' is just a regular 'k' in this case, like in 'cat'.
The 'v' is pronounced like in 'vast'. Putting the two together might be the tricky part

kv ... kv ...
The following 'a' is a long one, like in the word 'far'.
And then the 'r', almost the trickiest one for many foreigners. But what's funny about it in this case, is that in many Swedish dialects the 'r' in Husqvarna isn't pronounced at all. So don't feel ashamed if you skip it as well

So something like Hus-kva-na.
The 'n' is a regular n like in 'night'.
And the final 'a' is a short one, close to the pronounciation of the 'u' in the word 'cut'.
Husqvarna - Hus-kva-na
Now go ahead and practice!
Cheers! /BeO