IconVault's TLS Lab lets you step through the TLS 1.2 and TLS 1.3 handshakes message by message, from ClientHello to Finished, with an animated client/server diagram showing exactly which messages travel in which direction and what each one carries. Play, pause, step forward and backward to study the exchange at your own pace.

Everything runs in your browser with no signup, and it is completely free, which makes it ideal for students, interviews and curious developers. The honest note: this is a simplified educational model, not a real cryptographic implementation, so it explains the protocol flow rather than the underlying math.