Many times a piece of text will give you some of the details while withholding some others. The author's purpose may be to keep the reader's interest by not stating the obvious, to add suspense, or to "show" rather than "tell" through language the reader can enjoy. If a piece of text says, "Laura told Ben she had to go home early. She had a hand on her stomach and her face looked flushed," we can infer that Laura is physically ill. The author doesn't need to state this fact and trusts that the reader has been given enough information to work this out on her own.
At times you may come across a word you don't recognize in a piece of text. This is occasion to draw an inference. Look at the rest of the sentence and other sentences nearby, to see if you can figure out the definition. If a sentence says, "Joe was quiet, but his brother was vociferous," we can infer, based on the words "quiet" and "but," that "vociferous" means noisy.
Inferences are especially useful in understanding similes and metaphors. If a text says she was as "quiet as a mouse," you can use inference and common assumptions about mice to understand that that person is reserved and does not call attention to herself. If the text says, "he is a rock," you know the author doesn't mean that literally; instead, you can think of certain characteristics of a rock, such as impassiveness and hardness, to understand that the author means that "he" is stoic, or strong, or impossible to move.
When making inferences, it is important to be mindful of bringing too much of your own opinions into a text. Inferences should be based on clues the writer provides in the text, not on the reader's preconceived notions or beliefs. If you read a news story about a political candidate you support and assume the writer shares your political opinion about the candidate, even though there is no evidence of that bias in the text, you are making an illogical inference. Logical inferences always have some textual support.