Locate the output jacks on the rear panel of the Tascam DAT recorder. Often, there will be different types of outputs, usually RCA (unbalanced) outputs and XLR (balanced outputs). Depending on your interface, you may chose either one.
Connect the audio output from the Tascam DAT recorder to the input of the audio interface with the output cables. Your audio interface may have different connectors than the output of your DAT recorder. M-Audio and Line 6 produce audio interfaces that offer several different inputs, usually balanced 1/4" TRS Connectors and balanced XLR connectors.
If the output of the DAT recorder is a different connector than the input of the audio interface you may need to implement an adapter that changes the cable to the appropriate connector. RadioShack or other electronics stores will usually supply a wide variety of adapters.
Insert a tape into your DAT recorder. Press play.
If your recording software has the appropriate inputs selected to take input from your audio interface, you should be able to monitor the signal now coming from the tape in DAT recorder.