You're talking about one thing with a bass reflex speaker: a ported design if the shape of the speaker is round, or a rectangular design if it's vented. A DIY bass reflex speaker cabinet can be built in two ways. The simplest is to buy a ready-made cabinet, and install your own loudspeaker and components. The other way is to build the cabinet from scratch. Download speaker-building software, and base the cabinet design on the biggest loudspeaker to be contained within the cabinet. Either way, a DIY bass reflex speaker cabinet is less expensive than buying a ready-made speaker.
Visit Madisound, Parts Express, or any other site that sells empty and unfinished speaker cabinets. Even if you don't buy a ready-made cabinet, seeing how they're configured and made is beneficial.
Buy birch plywood as your box material. Birch plywood was the material of the most famous speakers ever made, in the days when medium density fiberboard (MDF) was not even thought of. It takes screws better than MDF, is more economical and is lighter in weight.
Download speaker-building software. There are free downloads available that do all the calculations for you in terms of the type of cabinet you are planning to build. The complicated measurements are all taken care of by the software.
Base your design on the largest loudspeaker in your cabinet and saw the wood pieces on a table saw. Alternatively, you can have the wood cut at the place where you purchase it.
Build the basic box first. This includes the sides and top and bottom. Tops and bottom pieces are generally inset within the sides. Glue them with good quality wood glue, and then further strengthen the bond with wood screws drilled into the joint every three inches.
Make the cutouts in the back panel. The back panel usually includes a terminal cup to connect speaker wires from an amplifier. Make the cut out with a jigsaw. Then, affix the prepared back panel to the cabinet box, gluing and screwing it against the edges of one side of the cabinet.
Prepare the front panel. This involves making the cutout for the speaker or speakers, and creating the port or vent if you are using one. A port is generally round; a vent is usually rectangular. Vented cabinets are somewhat larger than sealed enclosures, and it is in this area specifically that speaker building software is a huge timesaver.
Attach the port or vent before attaching the panel to the box. Attach the panel with the same glue and screw combination as used on the rest of the cabinet. After connecting the panel, run a bead of silicone caulk along all interior angles to create an airtight seal, and allow the caulk to dry for at least 12 hours. Silicone caulk emits gases while drying that will damage speaker surrounds.
Attach the speaker using speaker wire to the terminal cup's connectors. If you're building more than a subwoofer or single speaker, you will also need to include a crossover in the box. Once the wiring is attached, use wood screws to attach the speakers to the front panel. Run a bead of non-drying caulk around the woofer perimeter to ensure an airtight seal.
Sand the entire cabinet, then finish it with paint or stain.