I have never done the swap myself but in reading about it from those that have, there are quite a few areas to be considered.
-tranny cross member. Also crossmember frame extension if very early '66.
-tranny linkage. If car now std, column change or floor shift install reqd as well as pedal change.
-rad must be changed to bigger unit which may require battery box change as well to fit.
-front springs must be upgraded to handle the weight of the 390.
-front sway bar upgrade to 7/8 or 15/16 minimum reqd.
-possible rear spring upgrade.
-will now have 8" rear end which will work if not pushing engine. Otherwise need to upgade to 9". Gear change may be desireable.
-If wheel/tire size now stock, upgrade recommended.
-Brake upgrade, especially the front strongly recommended.
-torquebox and frame inspection.
This list is by no means all inclusive but as mentioned, these are areas that others have found either required change or have been considered to be areas where change is likely to be required or recommended for street use.