The I/O is a basic serial two-wire clock/data connection. It consists of a DIN external clock input, a CS enable input to start the conversion, a DIN serial input for control data ( 8 bits per Tables IV sent before each conversion) and a DOUT for the A/D output data. The input and output data is synchronized to the clock.
Basically, in operation you generate a low CS signal to start the conversion, input the 8 control bits, and then read the A/D digital output word.
The ADS7834 is operation is not simple, but it appears fairly straight forward. Just keep reading the explanations along with the diagrams. The information is all there, if perhaps a little cryptic in spots. Try to digest a little at a time. Read a small part and refer to the diagrams until you understand that portion. (Sometimes it's easier if you make a separate copy of the diagrams so you can more easily refer to them while reading.) Generally every sentence conveys an important piece of information. Skipping or skimming some of the data sheet often results in missing something important. Technical data sheets are usually written in a sparse syntax with few filler words or elaboration. It is in "plain english" but probably only to an engineer.
This is not something you can necessarily expect to understand in an hour or two. The old gray matter needs to be really exercised. Eventually it all will make sense.
If you get hung up on a particular question, place a post and someone can likely help.
And once you understand this device, understanding the next one will be a lot easier.