How can I get my Sony Handycam DCR-SX44 to work with my Mac?

Take a look at this page to determine if your model is compatible:

http://help.apple.com/imovie/cameras/en/index.html?lang=en_US

If you can't get it to work, post back - as long as you can get your memory card to appear on the desktop, you can use something like MPEG Streamclip to convert the video to a format iMovie can work with.

I have this camcorder. Just connect it to your Mac, open iMovie and click import button:

That's all.

will this allow me to put it on a dvd?

It will need to be rendered and exported either to iDVD (if you have it) or another burn software such as Roxio Toast for encoding and burning. The finished product should be playable in any DVD player.

did you to buy a firewire cable

I did not need to buy one because my setup is different (I don't have a Sony and I import from my Canon's SDHC card); however, if your camera has a FW port (IEEE1394 I believe), and didn't come with a firewire cable, then yes, get one.

You do not need to buy a firewire cable, because this model works via USB cable, and iMovie recognizes it.