It is easy to glue MDF to wood with some construction adhesive and clamps. MDF stands for medium-density fiberboard and cuts and handles similar to wood. PL-400 is the most commonly used construction adhesive and bonds to all sorts of surfaces, including wood, concrete, metal, plastic and PVC. It is easy to work with and extremely strong.
Dry fit the MDF and wood pieces together to make sure that your fit is correct. Once you apply adhesive, there will not be time to recut the materials.
Place the PL-400 into the caulking gun and open the tip of the tube. Squeeze a thin bead of adhesive along the desired area and place the MDF onto the wood.
Clamp the two pieces together. After the adhesive has dried, remove the clamps.