I haven't used a Tivo, but obviously all the streaming components to/from Tivo are not available on the DVR.
DVR can record 2 shows at a time, but you must watch one of them (live) or you can watch a 3rd recorded show at the same time. Recording happens using the Cablevision Guide. If you have a live show (like wrestling) that runs over it's alotted time into your time slot, your going to miss the end of the show. You can pause and rewind live TV. The service is $10 / month, but in the absence of Tivo, it's better than nothing. It can record any premium channel that you subscribe to, and the remote it fairly simple to figure out.
Sorry - like a giant run on sentence, but that's the brain dump. Recording has a couple of options (keep for 14 day or until I erase), it will automagically erase any shows that have passed the 14 day mark. You can set up custom programming to copy an entire block of time. You can also just press the record button to record whatever your currently watching. Handy when I'm about 3/4 through some random show and I have to run out for a little while.
Whew... If you have any specific questions, let me know.