I've found a nice bit of assembly in xv6 https://github.com/chrisdew/xv6/blob/master/bootasm.S which shows me how to move from 16 bit to 32 bit protected mode.
Does anyone know of a similar example for entering the 64-bit mode? (Either through or without using 32 bit mode.)
In order to enable 64 bit capabillities, you must switch the CPU to Long Mode.
To enter Long Mode on a 64-bit x86 processor (x86-64):
If paging is enabled, disable paging.
If CR4.PAE is not already set, set it.
Set IA32_EFER.LME = 1.
Load CR3 with a valid PML4 table.
Enable paging.
At this point you will be in compatibility mode. A far jump may be executed to switch to long mode. However, the offset must not exceed 32-bit.