While it's not easy to find a painting by searching by its description, you are likely to be more successful if you use specific terminology to identify key features of the artwork. Genre, period of history and what is happening in the painting are all important features.
First, identify what genre the painting belongs to. Five traditional classifications of paintings are history paintings, portraits, genre-paintings (everyday scenes), landscapes and still life. Second, take a guess at what period of history the painting is from. Are the figures stylized or realistic? What type of clothing are they wearing? Lastly, notice prominent features and colors depicted in the painting. What seems to be the main subject? What is happening in the painting?
Take your observations, narrow them down to keywords and string them together. For example, helpful search terms could be "realistic portrait Renaissance woman white earring." Click on the "images" section of your preferred search engine, and see if any of the results match the painting you are trying to identify. Once you find a match, click on it to discover the name of the artwork and its painter. "Realistic portrait Renaissance woman white earring" will lead you to the famous painting "Girl with a Pearl Earring" by Johannes Vermeer.