Aside from the faux leather itself, which may absorb some types of glue, plywood is also a porous material, which can make keeping glue on the surface long enough for the faux leather to stick difficult. Though most adhesives will usually work without any additional materials, you can help the glue stick by creating a less porous surface on the wood. One way to do this is to coat the plywood with waterproof sealant prior to beginning a craft project.
Adhesive known as super glues, including the Super Glue brand and Gorilla Glue, have stronger bonding properties than standard glues. These glues also dry more rapidly, which shortens the time that the glue has to absorb into either the faux leather or the plywood before it has a chance to stick. When working with super glue, avoid getting the glue on your skin or other objects because it can be difficult to remove.
Hot glue has many of the same basic properties as super glue, including a quick drying time and stronger bonding than traditional glues. The glue comes in solid sticks which are melted down and applied with a glue gun. Once applied, the glue cools back into a solid again, forming a sturdy adhesive. Working with hot glue does present the possibility of injuries from burning, but, unlike super glue, hot glue peels right off most surfaces.
Spray adhesives are another option for gluing faux leather to plywood. Like both super glue and hot glue, spray adhesives are quick dryers, generally sticking in only a few seconds. Some companies make spray adhesives specifically for fabrics. These adhesives work well for attaching faux leather to most surfaces, including plywood.