I need to know how to properly install a gear shift selector cable

Yes it is a ballpost and socket, and my shifter is on the floor.

No. It's not snapping on, it may have been removed badly by the mechanic who put my transmission in, ( like pliers or something)Is that possible that a part of the socket has been altered or broken off and I cannot see that?

There is a small metal insert that goes in that socket that makes it snap but you might have better luck finding the whole cable

It appears that is exactly what I must do. Now tell me what I have to do to properly install that cable.

Is it a column shift or floor shift? If its a floor shift its simple just fallow the cable from the transmission to the fire wall and make sure it is not hooked or fastened to any thing. Then go in the car and take off your shift knob. Look over the plastic around the shifter and make sure there's no hidden screws. Most of it just snaps on. Then detach the other end from the shifter and simply pull it out

If its a column shift fallow the same steps except your removing the lower dash panels ( usuallyfastened with T-15 torx screws and 6.5mm hex bolts ) until you find the other end of the cable and can remove it from the shifter