It is very doubtful that it is smoke. It is most likely steam. Either there is a pinhole leak in the radiator allowing hot coolant to escape that then vaporizes into steam when it hits the atmosphere... or there is something spilled on the radiator that steams when the radiator gets hot. Have the radiator pressure tested for leaks.
I would suspect a clog in the radiator.
The Radiator fan relay has probably failed. It is bolted to the lower side support next to the radiator.
radiator termostate
there is no real radiator cap. On the left side of engine compartment there is a coolant jug. This where you would add coolant to radiator.
The radiator drain plug on a 1988 Honda Accord LX is located on the lower right side of the radiator. If facing the vehicle from the front, it would be on the driver's side of the radiator. To drain easily, loosen the radiator cap after opening the drain plug.
The right side (passenger side) would be the transmission cooler lines. The plastic radiator tank is probably cracked near or at that fitting. Replacing the 12 year old radiator would be best.
ANSWER: On the lower left side of the Radiator (passenger side).
either the transmission oil line to radiater is not tightene or the oil cooler tank at bottom of radiator has a leak
some times the fan will not work if the radiator fan sw is bad. this is like a oil presure sw when it get to the right temp the fan sould start up. it is loc on the side of the radiator.
The plastic tank on the side of the radiator can be replaced but it would be quicker and cheaper to just install a new radiator.
Your water pump is bad
would the tierod cause the wheel to turn out