ARP Becomes Neighbor Detection
To translate layer 3 IP addresses into layer 2 MAC addresses, the Address Resolution Protocol (ARP) was used in IPv4. In IPv6 a similar mechanism is used and referred to as Neighbor Detection (ND). In addition the good practice in IPv4 networks to check if an IP address that was assigned is already used by someone else by sending an ARP message prior to using the IP address is now a feature in IPv6.
DHCPv6 and DNSv6
As discussed in the previous post, the IP auto-configuration functionality does not supply a DNS address to the host during startup so it can't translate domain names into IP addresses. Therefore, DHCPv6 is likely the means to get this information, potentially together with the IP address of the default gateway and further IP addresses for the interface.
The current DNS service also gets an IPv6 counterpart because it has to deliver IPv6 addresses for a request. While in DNSv4 an 'A' record query is used to translate a domain name to an IP address, DNSv6 uses AAAA records. The four 'A's stem from the fact that an IPv6 address has four times the size compared to an IPv4 address.
Routing pretty much works as in IPv4 but has been simplified as the network and host part is fixed in IPv6 compared to net masks of different lengths and classless inter domain routing (CIDR) in IPv4.
Tunneling IPv6 over IPv4 and Vice Versa
Needless to say that IPv4 and IPv6 can coexist on the same interface. In most cases, however, networks only offer IPv4 today. To access IPv6 hosts from an IPv4 only network today, IPv6 over IPv4 tunnels can be used for the purpose. There are several different variants but I won't go into the details here.
IPv6 only networks could also exist in the future as well. Should it be necessary for a node in such a network to reach an IPv4 host, IPv4 over IPv6 tunnels exist as well.
So that's my crash course overview of IPv6 for now. Agreed, this is very very simplified but I think those are the main concepts you need to get your head around from an end device's point of view. Next stop: How IPv6 is integrated in 3GPP.