Jamie is right on. ill toss more info out, as it sounds like you are a little lost. the stock solenoid has one hot-side terminal (with all the cables on it) and one switched side (only the large cable on it - cable goes to the starter in oem configuration).
now you have a second solenoid on your new mini starter. so disconnect the battery (should be already. to prevent shorts). if you can, move the single cable that is on the stock solenoid, to the other side (with all the other cables). this is where Jamie is saying you might need a newer model solenoid, to accomodate the additional terminal on the solenoid lug).
get some wire and connect one end to the now barren oem starter solenoid lug (you just took the cable off of it and moved the cable to the other side). run your wire to the new starter's solenoid. put it on the spade connector (might say 'activate' or trigger or something).
so now, operating wise: you turn the key to start. the interlock devices all work, juice goes to the thin wire on top of the oem starter solenoid. the solenoid switches, and sends juice down the wire you ran (from the once barren lug) to the new starter's solenoid. this switches the solenoid on the new starter. you have battery power hooked to it already (when you moved the single big cable on the oem solenoid to the other side with all the other cables). so it should start.
Jamie, et al, does this sound right? (i have not done one of these, so im using my [usually flawed. LOL] logic to try and help him out).