How do I attach a new pipe to this vertical ABS pipe?
The ideal solution is to cut the pipe and insert a Tee. You'll have to lift the upper part of the pipe enough to slip in the T junction and then lower the pipe down into the T and glue it. Sabre saw works to cut pipe, but it makes the pipe wobble a lot, which is not a good idea, it could break the tee fitting shown in the picture.

I would rather secure the pipe to make sure it doesn't move, perhaps cut a length of wood to place between the pipe and the background, and then gently cut it with a hand saw. Less risk of damage this way. Make sure to be really careful when you cut the last bit of plastic, that's when the saw gets caught between the two halves and snags.

If that is not possible, I'd use this kind of fitting:



You get the idea. Drill into the existing pipe with a hole saw, then slap this fitting on it with enough glue to make it stick. I'm not really a fan of these though. They're supposed to work fine if properly applied, and they sure come in handy when there's no other choice, like when both ends of the pipe can't be moved...

Also check your code.

EDIT: It is called a "Saddle Tee" -- google that, there are several types so make sure you pick the correct one, especially wrt pipe material.