Terminal node controllers are the “classic” approach to doing packet radio. They are basically dedicated modems that are used to implement a set of features that allow you to send and receive AX.25 formatted frames over amateur radio. The thing is: they are getting harder to find. My TH-D7a has a fairly sophisticated one built in, but if you have an ordinary HT, you’ll find yourself spending up to $100 or more for a packet modem.
Or, you could build one from a PIC microcontroller development board for $25 or so. My friend Richard is interested in doing this, I might have to give it a whack myself. While devices like the TinyTracker and such can be used to send packet radio, this one can also receive packet, and can act as a digipeater or dedicated APRS node. Neat!