The datasheet gives you wiring diagrams for the bridge and a circuit for driving the heater.
You'll need to add a circuit that can generate an accurate supply (they suggest 10V held within 10mV).
Then you'll need to add a differential amplifier to amplify the output and offset it to run into the Arduino's A/D. You'll need a reference for the Arduino's A/D - maybe you could derive that from the accurate 10V supply which will incorporate a reference.
Linearisation of the output you could do in software.
Hope that helps.
Personally, for a one-off, I'd either use one of the amplified modules or, even easier, the digital I2C one.
You could try contacting Honeywell and ask if they have a reference design.
Alternatively, you could develop a circuit for yourself - the elements of what is required are quite straightforward and you can find plenty of material on the websites of the major manufacturers of op-amps (application notes, etc). Try Analog Devices and Texas Instruments to start with.
