VoIP works by turning you voice into digital packets that are transmitted over the internet, these packets are then reconstructed and turned back into into voice the other end.
Yes you get a new phone number for incoming calls.
No you don't have to have your PC to make and receive calls if you use a proper device.
If you don't want your PC to be on to make and receive calls then you can either use a router with built in VoIP ports, or and ATA (Analogue Telephone Adaptor) which you plug into a spare port on your router.
www.sipgate.co.uk offers for no monthly fee an incoming number, of an area of your choice.
There is also
www.voipstunt.com and
www.sipdiscount.com .
www.voipcheap.co.uk can be used with an ATA/router, but you need to use the sip proxy of sip discount or voipstunt.
Gradwell as mentioned above is a paid for service, but is quite reliable.