IPv6 works pretty much the same way IPv4 does except that the address pool is considerably larger. From an end suer standpoint, it is transparent to usage like IPv4 is. It has the advantage that there are enough addresses you can assign every network connected device it's own address. This eliminates the necessity and some limitations of using NAT (networks address translation) used to extend the available address space. From a security and privacy standpoint it is a double edged sword. It allows the easier identification and remediation of a misbehaving, compromised or malicious device (as everything has its own address) but at the same time it uniquely identifies each device removing anonymity from the network, again since every device has its own unique IP.
To use IPv6, your ISP or connection provider has to be IPv6 capable and be distributing addresses. If they don't you can still get into the IPv6 game by using a tunnel provider like HE.com who lets you connect using an IPv4 address and relink out using IPv6. In simplistic terms it is an IPv4 to IPv6 NAT.
