The normal operation for an OTP is xor. Now if you reuse the random key K on messages A and B, you get encrypted messages A' = K xor A and B' = K xor B. Now, an attacker who learns A' and B' just needs to do A' xor B' = A xor K xor B xor K = A xor B. Since your input is not random, but structured data like natural language, this is now relatively trivial to break using crypt analysis since you essentially end up with something like "MEET AT DAWN" xor "I LIKE TRAINS".

Story time: The USSR once reused an OTP key (after years or even decades, can't recall), but a US' three letter agency had the old ciphertext (A') and reused that to break the new ciphertext (B'). They probably had some scheme with a broadcaster saying "use codebook 1234, the secret is GARBLED DATA". At least that's the story a cryptography lecturer told us (and the fragments I remember).