Like any column, there are three components to consider in the design: the base, the column itself, and the cap.
Romanesque
Romanesque columns are squat, square columns that typically rest on a trapezoid-shaped base. Their caps (or capitals) are often decorated with a floral motif. This particular type of column was used extensively in the mid-1800s. Like many old architectural designs, square columns are enjoying a revival.
Fluted
Although a basic square column is simple and plain, like round columns they can also be fluted. Fluting refers to columns with vertical "lines" carved into them, or grooves. Fluting is typically done on all sides of the column, although with a square column, you could have just one or two sides fluted. When you think of fluted columns, you most commonly think of the Doric column. Moreover, square columns can be divided in half, having fluting done on the bottom, but a smooth column on top. Fluting on square columns can also refer to having an inset rectangular design on each side of the column rather than vertical grooves.
Tapered
All columns, round or square, can have either straight shafts (the column itself) or be tapered at the top end. Egyptian columns were typically tapered then decorated with a lotus leaf design on the cap. Square columns can be tapered and have plain or decorated caps. You can either taper or flute your square column, but trying to have both will cause design problems.
Brick
One option for square columns, or pillars, that you don't see with round columns is building a brick column. Bricks lend themselves to creating square shapes over round. Brick columns work nicely on porches and covered decks. They could be used inside, especially if you have a bricked wall or fireplace to pull the look together. Most frequently, however, they're used outside.