Hardboard is also known as pressed board or Masonite. The material is compressed wood fibres mixed with a resin that typically leaves one side smooth and the other side rough. Hardboard is highly absorbent, which makes attaching two pieces together difficult. Standard gluing does not always adhere very well. You can use normal wood glue and clamping to join two pieces of hardboard, but you have to take a few extra steps to secure the final product.
Pour some wood glue into a paper cup and dilute it with water. Mix the solution with a paintbrush.
Apply the diluted solution to the two pieces of hardboard evenly across the surface. You want to coat the area of each board that comes into contact with another with a light solution. Allow the solution to dry for one-half the drying time listed on the bottle of glue.
Apply an even coat of undiluted glue to the same area.
Join the pieces together and attach clamps to hold the pieces firmly. Allow the pieces to dry fully for twice the time listed on the bottle before removing the clamps.
Hardboard is very absorbent. The above process allows for the absorbent nature of the wood. You can use an industrial adhesive, which has a lower water content than glue.