This is a piece of free-burning ABS tubing showing characteristic flame color and smoke. The burn test, as it’s known, correlates a plastic sample’s composition with a set of observable properties including…

1. whether or not the material will freely burn in air when a gas ignition flame is removed,
2. the color of the flame,
3. the smell,
4. the presence or absence of molten drips, and
5. the color and properties of any smoke, esp. the reactivity of smoke with wet litmus paper.

Though useful, the burn test should be used with caution of the toxicity of many plastic combustion products, and need not be a first resort when confronted with a sample of unknown polymer.

To risk stating the obvious, the first step in identifying a piece of plastic should be to look for a label. Since 1988, the SPI resin identification coding system (Wikipedia) has been widely adopted by plastics manufacturers to label their products for post-consumer recycling. Though the variety of possible plastic materials is essentially infinite, the familiar SPI recycling codes are a useful basic taxonomy of the polymers one is likely to encounter “in the wild.”

Assuming your sample has no label that would indicate its composition, then, the test which offers the best combination of safety, utility, and convenience is probably density. If your sample is made of a single material, solid through and through, its density can be checked against a set of reference liquids of known densities by simply dropping the sample in a small vial of each liquid: If it floats, it is less dense than the reference, and if it sinks, it is more dense than the reference. Polyethylenes and polypropylenes float in water (density = 1 g/mL), for instance, while most other plastics sink. Among heavier-than-water plastics, ABS and PS will float in glycerin (density = 1.26 g/mL), but PETE and PVC do not.

Other useful tests for discriminating plastics are the Beilstein copper wire test (which indicates the presence of chlorine, e.g. in PVC), susceptibility to acetone (most plastics besides polyethylene and polypropylene will become “tacky” on exposure), and whether the plastic turns white under stress, e.g. when bent (PVC whitens; PET does not).