Where can I find specifications for installing plastic culvert pipe (HDPE)?

In the NYS LTAP Center - CLRP Publication, Roadway and Roadside Drainage there is a good general description of culvert installation starting on page 53.

For detailed information, here are two possible specifications.

NYSDOT Standard Specifications
Look at section 603–Culverts and Storm Drains

Plastic Pipes Institute
Look at chapter 7

You can also check with your pipe supplier for information on proper installation. If not sure, go get some help from a professional engineer or certified contractor.