Not positive about an 1989 but I believe you will need to discharge the A/C system and disconnect all the lines going into the A/C and Heater core box mounted in the engine compartment. The A/C and heater core box and blower plenum under the dash are bolted together through the firewall. You remove the bolts and the two parts separate giving you access to the heater core and A/C evaporator. Go on the internet or e-bay and get yourself a service CD for that vehicle. I get them for about $10.
On my 88 (with AC) it was a simple remove and replace... Remove cover under right side of dash, drop computer down if necessary. Remove heater box cover bolts (various extensions needed). You have now found the heater core. From engine side, unclip the two heater hoses. Now remove core from inside the van. Reverse to install. If using a new gasket around the core, it can be a bear to push back in. Suggest new o-rings on the snap connectors. It didn't involve any part of the A/C system.
Because of all the helpful information from the folks here,
I Replaced my heater core on my 88 F150 last weekend.
Went thru the glove box.
Took off the cover plate.
Drained the antifreeze in buckets, engine cold.
Loosed clamps. Two of the clamps were stock, it was a bear to get off.
Cut off hoses, (I replaced with new ones).
Pulled the heater core out, replaced with new one.
Took me a verrrrrrrrrry long time to do this first time project.
Old Besty is up and running again.