Ryan,
this forum is IPv6 related, your question is strictly IPv4 addressing.
I will give you a few details (everyone has to start somewhere) and I hope I am not annoying anybody, but I would recommend a good primer or even a must read book (Edward Comer Internetworking with TCP/IP just volume 1) if you want to get somewhere with routers/firewall and the sort.
RFC1918 defines private address space as 10.0.0.0/8 172.16.0.0/12 and 192.168.0.0/16 which means any ip address that begins with (we need to use binary notation for this) 00001010 or 10001100.0001 or 11000000.10100100 belongs to private address (note the number of bit is exactly what has been indicted in the RFC after the /).
In dotted decimal this is 10.x.x.x 192.168.x.x and for the 172.16 is a bit more complex because due to the conversion and the addressing space not lined up with octect the 172.16 space is the union (in the mathematical sense) of 172.16-31.x.x.
Concerning the network classes those are defined by the firts 2 bits of the IP address:
0x class A
10 class B
11 class C
So as you can see in private space you have 1 class A 16 class B and 256 class C networks. All of this is kind of obsoleted by CIDR but that is another discussion.
Happy reading
Fabio