the ecu only donates the tachometer signal for the automatic operation. it is controlled by the atcu, a small box located under the dash to the right of the steering column. atcus vary from year to year and you need to be sure, if it is replaced, to use the same model year part when you change it. treat it like the ecu and do not disconnect or connect it with the battery cables connected. remove the battery ground first.
the shifter may be out of adjustment. it has a cable that operates the big multi-position switch on the front of the transmission and i have seen a number of autotragic cars have problems when people jerk the shifters around instead of operating them with a softer touch. the cable actually stretches when they get jerked into gear repeatedly.
transmission fluid and filter maintenance seems to be largely overlooked on metros, too, and that tends to gum up the pump bodies which gives them shifting problems. if you don't know the maintenance history just assume that the oil has never been changed.
like ralph said, pop the oval 2 pin plug on the left side of the car towards the rear of the transmission. jump 12 volts from the battery to the 2 connector pins (one at a time) and listen for the click as the shift solenoids pull in. the oil pan mutes the clicking so you may need to use a stethescope. the solenoids are grounded through the case so you don't have do anything but touch the connector pins with a 12 volt live wire.
i think that the best troubleshooting guide is found in the 92 fsm. it gives you step by step testing instructions and has very thorough diagnostic and repair sections.