Typically, print media uses the word 'infer' as synonymous with 'imply'. An inference is a tool of logic, alllowing one to move from premiss to conclusion. Deductively speaking, an inference must be valid (ie true premisses cannot lead to a false conclusion). Inductive inferences are not so easy to define, but are often supported by probability (the sun rose yesterday, the sun rose today, therefore the sun will rise tomorrow). Either way, to infer is to reach a conclusion based on an argument. On the other hand, to imply is to hint or suggest a conclusion implicitly (ie, not explicitly stating an argument for a conclusion). 'His language implied a dislike of x'.
I "infer" by receiving information and thinking about it; I "imply" by thinking up something and sending it out.