Over and over again I see IPv6 touted as being designed to handle 2^128 hosts, but this is not correct. Sure, that's how long the address is, but to say that its capacity is 2^128 is missing the whole point.
Let's look back at IPv4's design. It has a 32-bit address, but it is divided into a network address and host address. Which portion of the address is network and which is the host is specified by the network mask. There were three different network sizes specified: A, B and C. As the internet became more populated there were problems with assigning network address blocks and routing them properly, so they switched to classless inter-domain routing where more specific network sizes could be specified and assigned. This helped delay address exhaustion, but it made routing more cumbersome because there was no organization to which network address might be on which router, so the routing tables grew large and the routers spend more time figuring out where to send data.
With IPv6 we are still dividing the whole address into a network address and a host address, but this time they have made the address space large enough so the host address can always be the same size, and the network address can be routed in a much more efficient hierarchical fashion. People used to IPv4 seem to think that IPv6 assignments waste colossal amounts of addresses, but the aim is to have a globally unique host address plus a network address scope that will simplify routing for the foreseeable future and beyond.
The last 64 bits of an IPv6 address is the host address, and it ideally will be globally unique. Bit 7 is a flag to indicate whether the address is globally unique or not, so the host address portion has 2^63 globally unique addresses and 2^63 non unique addresses. Human-assigned addresses like 2001:db8::1 and 2001:db8::dead:beef aren't likely to inadvertently set bit 7 to 1. Unique host addresses are EIU-64 addresses which are basically a longer MAC address. In fact IPv6 autoconfiguration transforms the 48-bit MAC address to a unique 64-bit EIU-64 address.
Every subnet should be a /64, meaning it should have a 64-bit network address and 64-bit host address. (Network mask is /64 or ffff:ffff:ffff:ffff:0000:0000:0000:0000). One could specify and route smaller subnets, but it would break IPv6 autoconfiguration and go against the design of globally unique host addressing. If you have a larger block of addresses assigned—say a /48 like many tunnel brokers assign—still only use one /64 out of it for each subnet, or again autoconfiguration is broken, and have you really already used up 2^63 or 2^64 addresses on that subnet? I didn't think so.
Aside from the larger address space, IPv6 behaves much like IPv4. Some of the specifics look different but have analogous functions between them. For now I'll cover some of the more basic differences an end user might notice.
People are intimidated by the long addresses, as if 192.168.254.3 was short and intuitive back in the day. Really, how often does one type in an IP address? And how often are you not able to cut and paste it with a mouse? Moreover, there are multiple peer name resolution protocols (Apple bonjour, MS PNRP) that should further reduce the need to type in IP addresses. However, if you should find the need to type one in, you might need to enclose it in brackets when entering it in a web browser or other application, because the colon has special meaning. e.g. http://[2001:db8::1]/ or http://[2001:db8::1]:8080/ .
Linux ping utilities only work for IPv4, but they have ping6 and traceroute6 to use with IPv6 whether you're typing in the address or a name. Windows commands will work with either but have a -6 switch if you want to force IPv6 or -4 to force IPv4.
When looking at your IPv6 IP address you will likely find you have several, and certainly at least two. I will elaborate in another post, but for now be aware there may be link local addresses which are effectively local MAC addresses, the public address, possibly one or more "privacy" addresses, 6to4 addresses and Teredo addresses. In Windows you're usually wanting the "IPv6 Address" line listed under your main network adapter. In Linux you have fewer by default and want to pick the one not starting with fe80: through febf: .
Operating systems and applications have varying support for IPv6. Windows XP and newer have native IPv6, Windows Vista and newer has it enabled by default. Modern Linux distributions support IPv6 and may or may not have it enabled by default.
Windows XP cannot use IPv6 for file sharing or remote desktop, but Vista and Windows 7 can. Some applications would be capable of using IPv6 but don't recognize IPv6 addresses when you type them in. It can be hit and miss, but basic operating system support is pretty well established, and more and more applications are learning to accept and look up IPv6 addresses.