There are several methods that wine experts use to pair foods with wine. These methods always consist of evaluating the wine based on its flavor profile characteristics. You should identify these elements of the wine and try to pair them with a food that will be complimented or contrasted by those elements.
First observe how the wine smells, and what it looks like. There are categories of wine like white or red, and many subcategories and types throughout. Each type of wine may have a general taste profile of which to expand upon. Take note of how dry or sweet the wine is and then intensity of the flavor. Is the wine acidic or very tart? Finally, can you identify the dominant flavors in the wine, such as: fruity, nutty, smoky, buttery, herbal, floral, or earthy. Once you have developed a concrete flavor profile, you may now try to evaluate which food the wine will compliment.
There are some classics within wine and food pairing which you can start with as you develop your wine pairing method. Wines can either be used to challenge the taste of the dish or mirror it. Foods that are more fatty can typically be paired with a wine rich in tannins or tartness. It will help to cut through the rich and fatty dish. Foods that are buttery or velvety can be paired with a wine with similar qualities, such as Chardonnay, that will mirror the taste of the food and not overpower it. You may also pair foods high in acidity with wines high in acidity, such as a Reisling. But high acidity wines can also be paired with a meaty dish to contrast the flavors. Another classic combination is to pair sweet wines with the salt characteristics of cheese. Be careful when pairing with foods that are high in acidity or sweetness. Generally, you want the food to have the same or a lower acidity or sweetness taste than the wine you are pairing it with.
This short guide shows there are many different methods to use when pairing wine with food. You will no doubt continue to perfect your own technique as a sommelier in training.