Magic, and other similar workings, operates on the sympathetic action of Like attracting Like. In philosophy/spirituality things are linked by what they share in common through sympathy. What happens to one, is shared by the other. And even though the world of Physics tends to prefer the relationships of opposites, such sympathy and resonance can still be observed through simple experiments.
All you need is a pair of tuning forks to bring the idea of resonance to life. If they are keyed to the same note- the same vibratory frequency, you can place them on opposite sides of a room and set them both to ringing by striking only one. By doing this you are casting out sound, which is a vibration of the air, across the room at the same frequency that the other fork wants to vibrate at itself. So it moves in sync. It is their similarities that allow them to sing together.
Another observable example is by making waves in a pool of water. Make two sources of waves close to each-other and watch what happens when they meet. If the highs and lows of the waves match, where they cross they merge into a large peak. If the waves don't match in frequency they instead interfere with each-other. Sometimes crashing together, sometimes cancelling each-other out to some degree. Create a perfect opposite of waves and they simply cancel out into maybe a bit of a ripple.
Sympathy is additive- combine positive forces and they come together to build strength. The object of building up magical energy through symbols is like adding more and more tuning forks to a room. Or more waves to a pool. Under the right conditions you can add many small forces into one great combined and unified push. But to do so, first you need to gather your sources of those waves. Build up a collection of small tuning forks, and set them all to ringing so that the large one in the corner can sing along.
The trick is in learning how to figure out what any one thing might represent as a symbol. To that end, it is a matter of observation. Learn about the features, purposes/uses, and even behaviours of the animal or thing that your symbol comes from or resembles. Granted, some things are more abstract in their nature than others, but time and study makes the difference.
For example, consider something simple like a candle. Think about what they are used for, what they do, and how they work. And then reflect on how those details might apply to a desired concept or goal. They are a pillar of fuel wrapped around a foundation to carry a flame. As the fuel is consumed it generates light and heat in the form of fire, and with a byproduct of smoke. Now break down for yourself what qualities or concepts these are similar to.
Fire is a source of light- which brings sight by chasing away darkness. Light is synonymous with awareness and safety. It is familiar and comforting. It lets us see the world around us in situations where we would otherwise be blind. You can follow candle-light to its source, to navigate yourself to a destination. Or to let others see where you are so that they can find you. In this way a candle's flame can be a beacon to lead things towards you that you want to bring closer. Like calling over a friend (or friendly spirit). The light of a candle fills in dark spaces, chasing away darkness and likewise the comfort of light can chase away the dark energies of undesired or not-so-friendly spirits. And so it can be both attractive, and also repellent or protective.
Fire exists because of the burning of a fuel. It is a physical thing, like wax or oil, being combined and reacted with air to become something else. Transforming substantial wax into non-substantial gas and light and smoke. And so fire can be used to consume something physical, and convert it into non-physical energy and like smoke, release it to drift upwards. Like burning a note, transforming a physical message into energy and letting it drift upwards to intangible spiritual levels of energy and aether.
And that is just the flame! The wax, the fuel for the energy of the flame, is soft enough to carve or draw messages into that as well. Names, desires, outcomes, you can write them into the fuel, to feed the fire with your goal or message. You can colour the fuel, changing its properties to represent specific traits or ideas associated with the different wavelengths of the rainbow. Or you can meditate and stare into the flame of a candle to draw inspiration like a spark in the dark of your mind. You can watch the rise of the streamer of smoke, like a ribbon revealing the subtle ebb and flow of the air around you to dowse or interpret different meanings from changes or movements of the unseen air currents- a reflection of allowing you to add sight to the invisible.
Take any other object. Like scissors; an item designed to cut cleanly and safely with control. And use them to sever connections. String; Used to tie two things together into one, hold them in place, or immobilize something. Or a thicker wool or yarn might be woven together into a cloth or patch, one thread expanded into something greater by being bound onto itself. Or how about a Police officer's badge- a shaped piece of metal that is itself nothing but a shiny picture. But it represents authority and command because when we see it, we recognize it as a title for the person holding it.
Even (especially) animals can be very representative. Observe any single animal and you will find principles and qualities they can represent. How does that animal behave? What are its habits? What does it eat and how does it hunt? How does it find a mate or avoid a danger? Nearly any bird can fly through the air. And so a feather from that bird might represent the freedom of flight. No tether or restrictions but the ability of your own mind and body. An eagle hunts fish with sharp vision, being able to see below the surface of a body of water even from a distant height so they can dive down and strike, penetrating into what might be impenetrable to others in order to grasp and pluck out your target.
Heck, even something as incongruous as a drawing of a spiral on a piece of paper can have deep meaning, reflecting the cyclical nature of growth and learning through practice and repetition. A repeating circle that grows every time around like how practice is repetition but each time you start from a broader base of experience and familiarity. Or a square; Four sides for four elements held fast to their purpose. Or a circle; A complete cycle, a closed wall, a contained or containing surround, or even the natural cycles of the earth, sun, moon, seasons, and stars.
The key to Symbols, and using them, is to find relationships and similarities. Then use those relations to put an intentional, mental, and emotional link between yourself, your actions, and your goals. Place purpose and meaning to your actions and thoughts. If you recognize why a spell calls for lighting a candle, you can transition from just setting a flame to the mind-space of lighting a beacon. You can go from tying a couple dolls together to creating a representation of two people attached to each-other by their thoughts and emotions. And you stop being the person using scissors to cut a string. Instead you become a person of authority severing the unhealthy bonds holding two people together to set them free.
From now on, consider these sorts of things when you read or write a new spell. Or when you ask for or come across a list of potential symbols or representations. Don't just make a list of what they are, ask yourself why they are there, and how they fit into the purpose of the working. What does the symbol relate to? What action does it represent? Where does the use or relationship between symbol and goal come from? Consider these things, and not only will you come to understand much more than you used to, it will bring your workings to life within your heart and mind. This is what changes the practice of magic from a formula of actions into a living force of will.
You have your will which you wish to engage. You have a goal you wish to achieve. Symbols are the bridges that connect the two together- and that is when you have magic!