I will attempt to address your questions:
"I have a radio that is capable of digital. What do I need to complete the connection?"
This can be as simple as having a sound card on a PC interfaced with the radio - literally audio cables, in and out, from the PC speaker out to the radio audio/mic level in and radio line level/speaker level out to the mic of the soundcard. The key is isolation, so 1:1 transformers are necessary in many cases to prevent hum. You can build these for next to nothing or you can spend quite a bit on an interface that usually also has an interface to deal with push to talk on the radio. Its easy to use VOX (voice operated switch) to key teh radio and save quite a bit of cash
"What type of data can be transmitted? Is it text (like tty data)? Is it capable of transmitting files?"
Binary, Text, etc. RTTY (radio teletype) is based on a mark and space concept. CW (literally morse) is a true digital mode and it translates to text. There are a myriad of flavors. Keep in mind file transfer should be limited to UHF or VHF as a last resort because you have a very limited bandwidth at HF so throughput is low. Dont try to send a 100k file via PSK31 (using the cut/paste technique). Noise and trash would make this almost impossible at HF, but there are other options. UHF packet running 9600 baud (yes, 9600 baud... put that in perspective for a 100k file!)
"Is the communication point to point? My radio/computer to yours? Or is it available to all? If it is point to point how is it secured? PKI?"
Yes, Point to point or in the case of Winlink 2000 (winlink.org) you have digital radio communications interfaced with the internet so you are dealing with a network architecture and not just a point to point operation. Ciphers are prohibited and don't ever consider ANYTHING you put out over the airwaves to be secure. Someone (more than likely many) will be able to disassemble the stream
"Is there bridging allowed that would allow your computer to connect to another across the air and bridge to the Internet?"
Yes, see my comments about winlink 2000. This allows Internet email to pass via HF. I currently SYSOP a gateway node on a winlink mode known as winmor. It is a soundcard mode that allows a radio at my station to function as a hub/gateway for internet traffic. (winlink.org)
"Is communication facilitated through special software like the old terminal programs back in the day?"
UHF/VHF Packet can be controlled by hyperterm to talk to a hardware modem but many of the modes have specialized software to decipher what the sound card receives. Mode like RTTY can be operated with a soundcard where the Mark or space is actually an audio frequency shift or a hardward modem that facilitates an actual RF shift
That should get you started...
73,
MG