Plexiglass, also known as acrylic, can be attached to almost any surface mechanically or chemically. Plexiglass is often used as a substitute for glass because plexiglass is far more shatter resistant than glass and when plexiglass does break in breaks into a few dull-edged chunks instead of the hundreds of sharp shards that glass shatters into. Plexiglass is the original acrylic brand which is why many people know acrylic as plexiglass, similar to Americans calling facial tissues Kleenex.
Drill holes in the plexiglass at the points that you want to put bolts or screws through it to attach it to another medium. Standard metal drill bits can be used to bore through plexiglass with little resistance.
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Attach your carriage bolts or screws through the plexiglass and tighten them to the desired snugness which is dependent on the specific project you are working on. Plexiglass can be bolted down very tight due to its fracture resistance.
Apply plastic solvent to the plexiglass along the area that you wish attached to another plastic. Press the two plastics together and allow them to set for 12 to 24 hours to allow the plastics to melt together and then re-solidify.
Apply a small amount of silicone adhesive to the edge of the plexiglass and press it firmly against the material you want it fastened to. Allow the adhesive to dry and the plexiglass is now attached.