I need help connecting transistors to outputs on K8055

The open collector output acts as a switch between the digital output terminal of the card and the GND terminal. Actually there is a NPN transistor as a switching component. Its collector is connected to the digital output terminal of the card and its emitter is connected to the GND terminal. You can connect only positive voltage via a resistor to the digital outputs of the card. See example on page 19 of the K8055 manual: K8055 illustrated assembly manual (PDF)

To get your external NPN transistor on or off via the control of the K8055 card do following:

  • Connect the emitter of your 2N3904 to the GND terminal of the digital output block.
  • Connect the base of your 2N3904 to one of the digital output terminals (O1…O8)
  • Connect a pull up resistor (10k) from the base of your 2N3904 to the +9V of your power supply.
  • Connect the minus (-) of your power supply to the GND terminal of the K8055 card.

This way you get your 2N3904 on or off depending the status of the digital output where you connected it.
You can connect a LED with series resistor (1k) between the collector of the 2N3904 and +9V of your power supply.

BTW: Why are you using an external transistor? The digital outputs of the K8055 are specified to drive 100mA current and withstand +50V.