I would say first check if there is a schematic available and look for obvious connections, then in this order:
1. if there is an Earth connection on the power plug, check for continuity to the output wires. If there is continuity the PSU will be isolated from the line and neutral but obviously not Earth.
2. do the same for both line and neutral to the outputs, check for a resistance of at least 470K Ohms. If it's 470K or higher it probably is isolated.
3. if 1 and 2 say it's isolated, use a small 9V battery and 1K resistor in series, connect one side to line and then neutral and see if current flows from the other side to the output wires. Don't use 1.5V in case a bridge rectifier is in the input circuit, it may not be enough voltage to make it conduct.
It is quite normal to see a high value resistor and parallel capacitor between the neutral input and output sides of a PSU. They are there to leak away any voltage capacitively coupled to the output through the transformer. Without them, an otherwise isolated output could 'float' at any potential present in the input side of the transformer, often this is >300V so could momentarily cause damage if it discharges into a sensitive load. The resistor value is high enough to prevent a dangerous current flowing to the output but low enough to discharge the weak coupling between transformer windings. This is similar to the way an anti-static wrist strap works. The capacitor is also a low enough value (typically 470pF) that AC currents are kept at safe level but it keeps induced noise 'discharged' to a known point. Note that these components have to be rated for high voltage, often 1KV or more and are omitted altogether in power supplies used in medical applications where only extremely low leakage is allowed.
Brian.