Welcome to the "sane" world of Classic Civ2, Peaster! At least, the AI is a bit "saner" - you can keep a decent relationship going for more than 10 turns, and their attitude doesn't go from Enthusiastic to Hostile in one turn!
Under Game Options there is a checkbox for Move Units With Mouse. When it is checked your mouse has great power, but it must be managed carefully. If the unit is active it will blink (if not, click it ONCE). Holding the mouse over the center of it and moving it slightly toward one side of the box, the pointer will turn to a black arrow in that direction. If you click once at that point it will move in that direction (make sure you hold it still!). You can also click-and-hold on a different tile until the pointer turns to the word "GO" with a cranked arrow above it. When you let go it starts moving toward that tile, using the screwy CIV GoTo calculator (beware the DateLine!). If you decide not to execute the GoTo, slide the pointer back to the tile with the unit in it before letting go.
If you uncheck the box you can still use the 8 arrow direction keys on the keyboard (unless you have a compressed keyboard, like on a laptop).
Enjoy!