Select a tile size and pick tile colors that complement the permanent components of your room, such as sinks or bathtubs, major appliances like refrigerators or any furniture you plan to keep for an extended period. Reserve more colorful tiles for the border to enliven the room without overpowering other elements or putting excessive restrictions on future interior designs for the room. Select a tile grade appropriate for the degree of wear the floor will receive.
Create a mosaic pattern for your hexagonal tiles before you begin laying them. Use graph paper to work out your design. Account for the size of the tiles and the size of your room to translate your pattern to the actual floor or wall. Measure one length of any repeated patterns within the border and determine how many repetitions fit along each side of your border. Adjust the border's distance from the walls, as necessary, to accommodate the pattern neatly.
Identify which tile color is the predominant tone of your border. Take a sheet of this color and pry out individual tiles, adding back in pieces of the colors required to make your pattern. Use contact cement to hold the added tiles in place. Let the cement dry thoroughly before laying the tile sheets.
Lay the sheets of hexagonal tile in place if you are working on a floor. Confirm that the border is an even distance from the walls. Be particularly cautious in lining up any bends in the border, appropriate for hugging the walls of an irregularly shaped room.
Clear the area to be tiled and wipe it clean of any debris or dust. Use a trowel to apply grout to a small area of the floor or wall where you will start tiling. Begin with the corner of the floor furthest from the room's exit, or with the lower edge of the wall. Use hex tiles that are cut in half to align the edge of your tiled area with straight walls, bathtub edges or ceilings. Add a strip of square, rectangular or trim tile for a more finished look. Confirm that the lower edge of a wall is level before setting the tile. If not, draw a perfectly horizontal line on the wall and begin tiling there. Wipe off excess grout from between tiles with a clean cloth.