An intelligent living thing might attempt to communicate with us using some type of language:

• Their own language
• Our own language
• Music
• Symbols
• Mathematics (a universal language)

Its language could be conveyed by speaking directly with us, or it might encode whatever it has to say on some form of media. It could:

• Broadcast a message using radio waves
• Record a message on physical media (for example: vinyl disc)
• Encode a message within biological molecules (for example: genetic material). This is an effective way to store and possibly even hide a large quantity of data

Though we might not understand their language, we should be on the lookout for patterns or any signal that does not appear to be noise.