A testing facility should be able to help you decide which tests you will need and give guidance interpreting the results. Since soils vary greatly--even within one backyard--you will probably want to take a range of samples in order to get a better understanding of what might be in your soil. Check with the laboratory you will be sending your samples to find out how to prepare your samples and other requirements. Recommendations on how to improve your soil may be specific to what you intend to use the soil for (flower garden, vegetable garden, etc.).
Title: Urban Soils Lab at Brooklyn College
Organization: NYC Urban Soils Institute
Description: This affordable soil testing service is available to gardeners throughout the country. The Basic Soil Quality Test will report on pH; salt content; soil class; NPK (nitrogen/phosphorus/potassium) levels; lead, arsenic, copper, and zinc; and organic content.
Title: Soil Nutrient Testing
Organization: Cornell Cooperative Extension of Westchester County, Elmsford, NY
Description: Our local cooperative extension performs pH tests on submitted soil samples for $18. Scroll down to section B for soil pH test pdf form, which includes instructions for taking and submitting samples. Results are mailed within two weeks. Scroll further for information on additional soil sampling for nutrients.
Title: Cornell Nutrient Analysis Laboratory
Organization: Cornell University
Description: They offer a range of soil fertility analysis packages, as well as total elemental analysis (heavy metal screening), which suggested for home gardeners.
Title: Individual Soil Analyses
Organization: Cornell College of Agriculture & Life Sciences
Description: This lab offers a range of soil tests for nutrients and composition (not contaminants).
Title: How to Take a Soil Sample with Doug DeCandia
Organization: Bionutrient Food Association/Westchester Chapter
Description: A five-minute video showing how to take soil samples for testing.