How do I connect a Tascam US-144 Audio/MIDI Interface

It will be helpful if you describe the symptoms a bit more. I can only assume that Tascam, being an audio interface, does not produce any sound. If this is the case, then:

1) Check connections (it's dumb, I know, but you'd be surprised...). To check if your system recognizes the new audio device, open up Audio/MIDI utility (Applications -> Utilities). It will show available audio devices and their parameters.

2) If connections are OK, then go to Audio Prefs -> Global and make sure Tascam is selected as an audio input/output device for Logic (then you can load a demo song and try to play it back)

3) If Tascam provided any kind of its own software control panel (typically would install with the driver), open it up and check for muted outputs/inputs

well, by this point you will certainly figure it out (hopefully)

not to be rude, but this is really starting to get on my nerves!

Dude, it's not my fault, OK? So you'd better calm down.

This Tascam device obviously has a direct monitoring option, which means that if you connect a sound source to one of its inputs and plug your headphones into headphone jack, you MUST hear something (and it is absolutely independent of any software that you use). If you don't hear anything, then there is a possibility that: a) you forgot to switch it on (hence no lights, no nothing, as you say) or put up the levels; b) the device is broken.

It is not true that its manual refers to Windows only. There are actually sections about how to configure it in Mac OSX (see, I had the trouble to download the manual just to help you). As for Logic, everything you need to know is also in its manual ('setting up your system' section if I am not mistaken).

Just in case, have you reached the stage when you can select Tascam interface as Input device for Logic in Preferences -> Audio -> General tab? If you have, it means OS recognizes it and the driver works.

So next step would be:

1) Create an Audio track
2) Select the APPROPRIATE input (the one where you actually plugged in your instrument) as a sound source (have you done that?)
3) Arm the track for recording or switch on input monitoring

I don't really know how much more specific can one be here. Also, note that I assume your Mac is in good condition and everything works, including USB ports and audio/USB cables.

What seems to be a problem here? You take a USB cable and plug it into Tascam device, the other end you plug into your Mac's USB socket. Done! 🙂

Why doesn't it work? Well, consider installing a driver for it first. After that it should work. Also, does it have a manual with connection/driver installation instructions? It must have it. So, why not start with its manual?

Man, everything you need to configure your audio interface is in its manual. Check out Troubleshooting section. As for control panel, read Control Panel Settings. Basically, if you can hear what you play through the headphones connected to Tascam, then it's working OK and you should further configure Logic for using it.

In Logic you have to select it as Input device in Audio Preferences panel and arm audio tracks for recording or switch on Input monitoring to be able to hear what you play.

I have not used this exact model but have used similar devices. From what I can determine by checking their website the thing should "just work."

Have you downloaded and installed the most recent Tascam Snow Leopard driver from the Tascam website? Do you have the interface plugged directly into the Mac? If so, have you tried another USB port? Have you tried a different USB cable.