How do i take the heater core out of my 81 f150

Disconnect battery ground cable. 
Disconnect cable from temperature blend door and the mounting bracket from top of heater assembly. 
Disconnect blower motor and resistor electrical connectors. 
Disconnect and plug hoses from heater core. 
Working under instrument panel, remove 2 nuts on 1980---81 models, or 3 nuts on 1982---87 models, attaching left side of heater assembly and right side of plenum to dash.

On 1980---81 models, remove screw attaching top center of heater assembly to dash. On all models, remove 2 screws attaching right side of heater assembly to dash, then lift heater assembly out of vehicle. 

Remove heater housing plate attaching screws, nut and bolt and the plate. On 1980---82 models, remove 3 heater core frame attaching screws and the frame. On all models, slide heater core and seal out of heater assembly.

Reverse procedure to install. Good Luck and hope this helps