Hi Hun - if you are working on the paying public you will need insurance (or should i say you would be wise to get it!) as anything could happen. I personally would not risk doing a treatment on someone without insurance - it's like anything really - would you drive your car without insurance?
As Redduck says, i'm not sure how it would work just on family & friends - but that's up to you hun.
Most insurance policy's cover public, product & treatment liability - which pretty much covers all you need if working on your own. You can also opt to cover your equipment too. There are some good prices out there - I got mine from Salon Gold.
Incidentally, when I started in this sector, my main career was completely different to beauty, but I still got the insurance even though I was only working on a few people per week - albeit mainly friends & family.
Hope this helps xx