AppleTalk is a network protocol family created by Apple which predates TCP/IP. It contains different protocols for different uses: address resolution, address/name mapping, service location, establishing connections, and the like.

The protocol family is also often collectively referred to as DDP, which stands for Datagram Delivery Protocol. DDP is the core transport layer protocol of AppleTalk.

Netatalk implements the AppleTalk protocols to serve files over AFP and provide other services to old Mac and Apple II clients.

It supports EtherTalk Phase I and II, RTMP, NBP, ZIP, AEP, ATP, PAP, and ASP, while expecting the host OS kernel to supply DDP.

DDP is a socket to socket protocol that all other AppleTalk protocols are built on top of.
ATP, ASP, and NBP are implemented as statically linked libraries in Netatalk's libatalk shared library.
The atalkd daemon implements RTMP, ZIP, and AEP.
The papd daemon implements PAP, allowing Mac clients to spool to a Unix print spooler on the netatalk host computer.

Linux

The Linux kernel has had AppleTalk support since version 1.3.0, released in June 1995. See the Linux 1.3.0 Changes file.

The source code for the AppleTalk driver lives under net/appletalk in the Linux kernel source tree.

NetBSD

Kernel support for AppleTalk appeared in NetBSD 1.3 in April 1997. See the NetBSD 1.3 release notes

The NetBSD kernel comes with an AppleTalk kernel module, confusingly named netatalk, located under sys/netatalk in the kernel source tree.

Other BSDs

Kernel support for AppleTalk appears in FreeBSD 2.2-current dated after 12 September 1996, as well as OpenBSD 2.2, or openbsd-current dated after Aug 1, 1997.

However, both distributions removed the AppleTalk kernel modules in the 2010s.

Solaris

Historical versions of Netatalk (until v2.3) distributed code for a Solaris STREAMS module that implements AppleTalk.

The source code is located under sys/solaris in the netatalk source tree. It is written for the SPARC architecture.

Generic

If you would like AppleTalk support on another operating system, you will need either need a kernel module for your operating system, or a userland AppleTalk stack.

Look at the above Solaris STREAMS module if your operating system supports that framework.

Otherwise, look at the ddp code in NetBSD if your operating system is BSDish in nature.

If your operating system looks different than these two cases, you'll have to roll your own implementation.