Where can I find the plaintiff and defendant arguements from the abington v. schempp case (1963)?

Answer 1

You can find a summary of the parties' arguments in the published opinion which can be found in numerous places on the web, but the best unbiased and free source will be http://www.findlaw.com

You can obtain copies of the actual briefs that were filed by the parties directly from the Supreme Court.
http://www.supremecourtus.gov/oral_arguments/briefsource.pdf

Briefs from 1963 will not likely be available online.

Answer 2

Look in one of two places. First, visit your local law library and look in the Sheppard Case Citations volumes under that case name. Where the case was heard will tell you what volume to look in. Now if the case went up on appeal, it will be recorded in the appellate reports of that state. Also, you can sometimes find case information in the annotated codes and law reviews.
In this case the citation is 374 U.S. 203. The first number is the volume in the Supreme Court Reports and the second number is the page where the opinion begins.