How would I go about hooking this up to a DAW?

If you have a Behringer mixer, you would have to hook this up to your mixer via an analog input- that is, either a channel strip using line-in or a stereo/mono input, or 2-track RCA input. If you have the Behringer Q302usb mixer, you can chain the Main Outs (red and white RCA jacks) to the monotron by running an RCA to 3.5 mm stereo cable or adapter from the Monotron, then run the headphone out of the monotron back to another RCA input on that same mixer with an identical cable, or to another mixers RCA 2-track in. If you have a different Behringer mixer that has 1/4" jacks, you'll need a cable to go from the Monotron to a 1/4" jack. Basically you're going to need a cable or adapter to go from the Monotron's 3.5 mm headphone out stereo jack to either another 3.5 mm jack, 1/4" jack, or RCA jacks.

how can i hear one play before i buy?

Search for "Korg Monotron Duo" on YouTube. Here is Korg's official video: http://www.youtube.com/watch?v=ilSWwjuRrhw

what cord do i need to hook it up too a amp? and also what kind of mic?

It uses a 3.5mm (like a headphone/aux cable for a phone) jack for both input and output. If you want to adapt it to studio gear you'll need 2 converters from that to 1/4". The jacks are pretty close together though, if you're hooking up something like that, it might not fit - and you might be better off using a guitar delay pedal or some other delay intended for 1/4" use.

Someone stated that this does not have a speaker output. Can anyone suggest an inexpensive synthesizer that does have a speaker connection?

The Korg Duo Monotron does not have an integral speaker, but it does have an output for stereo headphones (1/8" jack) that can also be used for an output controlled by the volume control for a male 1/8" stereo jack connector to a male 1/4" mono jack for input to a standard guitar amplifier (male/male) patch cord. I use a 36" patch cord from the Monotron to the guitar amplifier input. (not mono/mono). There is also an aux jack input (1/8" stereo jack) for connecting a CD or MP3 player. (a 1/8"male/male stereo patch cord is useful for the aux jack input)