I find the teaching of the five khandhas (the aggregates) a really helpful way to see our empty, not-self nature.
There's a lovely simile from the monk Nagasena, explaining anatta (not-self). He describes a chariot: the wheel isn't the chariot, the axle isn't the chariot, the frame isn't the chariot. No single piece is "chariot." But when the parts come together, "chariot" becomes a convenient name for these parts functioning as one.
Similarly, "London" is only London through the coming together of various parts: the Houses of Parliament, the London Eye, Big Ben, Covent Garden, the streets, the car parks, the people moving through it. Ultimately, it's buildings, shapes and colours that we suffuse with meaning and call "London." Take away the name, and there's no separate "London" to be found, which starts to show the empty nature of names, labels and concepts.
We're much the same. What we call "self" is really the five khandhas moving together: form (the body), feeling (the pleasant, unpleasant or neutral tone of an experience), perception (recognising and labelling what's there), mental formations (the reactions, intentions and habits that follow), and consciousness (the bare knowing of it all). Look closely, and it's hard to find a "me" inside any of them.
With no fixed or isolated thing called "me," just a continual coming together of these parts, moment after moment, the sense of being a solid "me" starts to loosen. Not because we've been told it isn't there, but because when we really look, it simply can't be found. It's worth trying for yourself.