You will need the following - and the beauty of it is it's cheap to get started...
a. The premier software is ACARSD (its free), and you found the Wiki, so you have the link.
b. A simple scanner that covers the VHF air band will do just fine. No need for a USD500 scanner here.
c. A good short connection from the speaker output to your soundcard. Do NOT use a discriminator tap here - a discriminator is NOT used in AM reception (it's used in FM mode reception)
d. As for an antenna, a simple ground plane cut for around 131 Mhz will do just fine. If you already have an antenna that works well on the civil air band, that will also work.
That's about it. Make sure that your soundcard input (mic in, line in, whatever your soundcard is set up for - lots of differences here) is enabled (some software disables it as a default, and the user must enable it in Control Panel). A quick and easy test for this is to make the connection and tune to your local NOAA weather station. If you hear audio nice and clear through your speakers you're half way home. The wiki mentions this but it bears repeating, since it trips up many - for the most part most scanners cannot scan ACARS; this is because there is a very brief tone that is sent before the beginning of each message. If the software doesn't hear the tone, it will not decode. Most scanners - there are a couple of exceptions - have a squelch time that is too long to open up for a brief pulse, so while scanning, it's unlikely the tone would make it through.
Once you get your setup working on a single frequency, then try scanning - if it doesn't work well, you know why. Sit on a single frequency with the squelch open, so you hear noise in the speakers.
If you are using a laptop, you will need to build - or buy (RS, Best Buy, ect.) an attenuating patch cord. This is because the output from your speaker is far too much for the low level input your laptop will expect, and it will overload it. Too loud, and the software will reject the signal. Keeping a nice moderate level is paramount.
That's about it. 73s Mike