Symbolism is simply when an author uses a "word, place, character, or object" to mean something above and beyond the literal meaning (Dr. Wheeler, "Literary Terms and Definitions: S"). One example could be seen in the phrase "new dawn." Dawn literally refers to the start of a new day, but used symbolically, a new dawn can also refer to a fresh new start at life (Literary Devices, "Symbol"). Flowers are also frequently used with respect to symbolic meaning. Historically, a red rose was the symbol of Venus, goddess of love, so even today a red rose is understood to symbolize passion, love, and romance.
To find symbolism, you first want to get a thorough understanding of the piece you are analyzing and its themes. D. H. Lawrence's "The Rocking-Horse Winner" is a tragic tale about a materialistic mother who can only obsessively think about her need for money and feels no natural love for her children. As a result, her son Paul devises a means to find luck to bring her money in the hopes that it will earn her love. However, sadly, the end result is to make her only more desperate for more money, desperate to the point that her son overworks himself and dies. Hence, some themes found in the story are materialism, luck, lack of love, overwork, labor, and obsession. Therefore, in order to pick out symbolism, you'll be looking for words, characters, and objects that help represent these themes.
Two of the most obvious examples are the word money and the house itself. The word money is found all throughout the story, but is it only representing money? Or is it representing the materialism, obsessiveness, and lack of ideals and values that can be attributed to money? Since it's pretty obvious through the story that the mother values nothing more than money, money is representing more than money itself; it is rather representing the themes of the story. The same can be said of their house. Their house is described as being pleasant "with a garden" and as containing "discreet servants." Hence, despite the obsession for more money, the family is actually quite comfortable. Yet the house becomes haunted with the mantra, "There must be more money! There must be more money!" Therefore, does the word house simply refer to a house? Or does it symbolize the fact that house truly isn't a home as it should be and rather echoes the mother's obsessive materialism. Hence, it can be said that even the house itself is symbolizing the story's themes, such as lack of love, materialism, and obsession.