i won't do your homework for you, but i can point you to http://danml.com/pub/connect4.html
, where i have a working copy of the same game for you to inspect. it's not the best code ever, i wrote it in an afternoon, but it seems to work ok.
a row win is easy: cast the board into a string, each char meaning red or black or empty.
then you can simply String.match() that string to find a row winner.
a col winner is almost as easy; just transpose the board and again look for row winners.
the diag win was one that gave me some pause. one easy way is to hard-code all the diags, but that's cheap. I came up with a way to transpose the board in diagonals (both NW and NE), and once again used the string match() row-winner finder to examine the result for a winner.
all the win detection code spans from line 222-300 (ignore the comments).