Assuming that the resin is pure, you will weigh 0.1 g. of it & place it in 10 mL of , say n-octane, inside a stoppered test tube at room temperature. You will shake the test tube & then leave it for 24 hours. This is done to give the resin time to swell & then dissolve. If the resin is insoluble, you will place the test tube in warm water to see if there is a change. If the resin does not for a clear solution, then it is depicted as insoluble in cold & hot octane.
In general, solubility of a solid material in a solvent depends on (a) polarity of the solvent and (b) temperature. You may choose your solvent accordingly.
try first the merck index. it is a simple and good reference book. I don't know your materials but try to find Hansen solubility parameters for your resin. It helps to find the solvents that can be used. Like Mr. Nazar and Mr. Ashis told, resins normally takes time to dissolve.