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How does superposition work in qubits?

Okay, I'll admit it - I've been nodding along when people talk about "superposition," but I'm not sure I really get it. Every explanation I find either goes full math mode (|0⟩ + |1⟩ what?) or uses those dead/not-dead cat analogies that just confuse me more.

Here's how my classical-programmer brain keeps stumbling:

1. Regular bits are like light switches (on/off, 1/0) - got it
2. Qubits can be "both at once" - but what does that actually mean physically?
3. When people say "probabilities," is that just fancy talk for "we don't know yet"?

What I think might be happening (please correct me!):

Imagine a spinning coin - while it's in the air, it's not actually heads or tails, but some weird in-between state. Measuring it forces it to "pick." Is that close?

1. How do we put it in superposition?
2. Why does this help with computation?
3. If we can't see superposition directly, how do we know it's real?

Would love an explanation that doesn't require a physics degree! Bonus points if you can relate it to something in classical computing.