Someone who wishes to indicate mild to moderate boredom during a conversation will speak in a monotone at a moderately slow rate (but not as slow as someone who is sad).
They often avoid eye contact (as if they’re looking around to find someone or something more interesting), and significantly decrease their other active listening cues.
They are likely to unconsciously or deliberately increase self-stimulatory behaviors (scratching, playing with hair (but not in a flirtatious way), shifting their weight or squirming, biting their lip, etc.), showing that the conversation is not stimulating enough to hold their interest. Beginning another simultaneous activity (doodling, e.g.) is a conventionalized way of signaling boredom, as is looking at a clock (or watch or cell phone, etc.)(although this may simply serve as a reminder of a relevant time constraint).
People who are bored may sigh audibly, and their body posture and facial expressions may appear mildly sad. They may orient their body away from the person who is boring them.
If someone is very bored, they will likely become impatient and annoyed with the situation and/or with you. Impatience is basically a blend of boredom and annoyance. The signs of boredom will become more intense, but the posture may become aggressive, words will be pronounced in a more clipped (formal) way (“spit out”), and the gaze will become more intense and challenging (as described for anger).