You just need to add a check when you're changing the position to make sure it hasn't moved off the edge. If it has, you set the position to the other side of the screen.
For example when moving left, you could do something like this:
LEFT:
SUB COL, 1
CMP COL, 0
JGE LEFTOK:
MOV COL, 79
LEFTOK:
You subtract 1 from the column position. Then you check if it is greater than or equal to 0. If it is, you're ok. If not, you set the column position to 79 (assuming the screen is 80 characters wide - you want to make a constant for that or look up that value).
You can do the same thing for all the other directions.
Strictly speaking you don't need the CMP COL,0
in the example above, since the SUB
will set the appropriate flags anyway, but I think the code is clearer this way.