is this program free to download anywhere?
Yes, there are a few options open to you regarding free software for this purpose. I personally, use Logmein which seems to work fine. I've only ever tried using over Windows based systems so it may be worth having a quick peruse of their website to check Mac support.
'Go To my pc' is another one, although rumoured to be not quite as secure during remote sessions as Logmein. Both of the aforementioned are free and should work fine, however both will require an active internet connection over you Lan.