Connecting quadrature encoder with differential line driver output

I'll need to "decode" this signal somehow into an A and B channel, which I can connect to my Arduino Uno.

Does anyone have experience doing this? What wiring is involved? Do I need a pull up/down resistors (I'm assuming I don't)? What components will I need?

Since the encoder has a differential output, at the minimum, I'd start with a differential line receiver. There are numerous variations on this theme - dual, surface mount, etc.

Data sheet show two voltage outputs available and optional formats.

Is a differential output fully TTL? As in, is a logic LOW actually between 0-8v, or is the wire left floating? The datasheet isn't at all clear on this, but I'm assuming if it is TTL, I can connect it directly to the receiver, and then Arduino without needing any resistors, etc. Is that true?

According to the data sheet it depends on which exact type/output you have (the seventh digit after the E23 part should give this):

Code 5: Electrical
0 5-26V in; 5-26V Open Collector w/2.2kΩ Pullup out
1 5-26V in; 5-26V Open Collector out
2 5-26V in; 5V TTL Totem Pole out
3 5-26V in; 5V Line Driver out (7272)
4 5-26V in; 5-26V Line Driver out (7272)
5 5-26V in, 5V Differential Line Driver out (4469)
6 5-15V in, 5-15V Differential Line Driver out (4469)

Outputs are described in a bit more detail at the start of the data sheet:

Outputs:
7272 Push-Pull: 40mA, sink or source
7272 Differential Line Driver: 40 mA, sink or source
7273 Open Collector: 40mA, sink max
4469 Differential Line Driver: 100 mA, sink or source

The high level you get is normally the same as (sometimes a tad lower than) your supply voltage, so if you provide 5V in, you get 5V out. You're not going to get a higher voltage out.

The Differential Line Driver output is what I want, however it doesn't specify whether it's TTL or not. If I provide it with 5V, what is the High and Low range? Is Low just a floating wire?

It says "sink or source" doesn't it? So that'd be driven to either GND or Vcc.

Besides, I've never seen floating for low. Only floating for high (open collector aka open drain). Regardless, it's easy enough to find out, and all that's needed in either case would be a resistor.

Right, so in this case we have an “active” interface? If it sinks and sources, I guess I won’t need any resistors, and can hook it straight up to a differential receiver (which accepts the correct voltage, of course)?

Indeed. That's the idea.