I'm helping my nephew do a short family tree that he's doing for a school assignment. My grandparents divorced and my grandmother remarried. Is there some standardized way that a divorce and remarriage is written on the form? What is it? And should her second husband be on the form somewhere?

While many people like to use their own designs for visual interest.. the basic "tree" (or pedigree chart) is for tracing direct lineage back. I am assuming that grandma's first husband is the actual parent, so he is who would show on this style of chart. Grandma shows also, but using her maiden name (since that links her back to her parents, further on the chart). In this usage, 2nd husband does not properly show.
The 2nd form used in standard genealogy is called a family group sheet.. this one shows an immediate family.. husband, wife, and children.. but ALSO includes relevant info. That means names of both parents of the husband, and the wife. Other children of the (grand) parents are not here. those show on their own family group sheet. On this sheet, one would add a line like "married 2nd John Jones" with maybe the date and place of that marriage.
If John and grandma then have children from that marriage.. they appear on a family group sheet of their own.. where John is now the husband and grandma the wife. (with note again.. grandma md 1st.. to link it to the other group sheet).
All of this is built into standard genealogy programs.
www.familysearch.org is the LDS church site, and they have an excellent free program called PAF that you can download in a few minutes. It stores the information, and can print the charts out for you.