For building things out of acrylic/plexiglass, you would want to use a solvent, usually something like weld-on #4The edges of your peices have to be relatively smooth, so you get could capillary action when applying the solvent. The solvent will pretty much mend the peices together permantly.

Here is a good video on basic acrylic working.

http://www.youtube.com%2Fwatch%3Fv%3...wNkRmve-tzHQAQ