At the beginning of Part Two ("The Sieve and the Sand"), Montag is pleading with Millie to open her mind to what books might be able to tell them. Montag supposes that books might contain knowledge and answers to his many questions. The problem is that he has never read before. Therefore, he has no critical reading skills, no critical thinking abilities - because he's never read and thought like this before. He reads but just can not retain any of the information he reads. In time, he would be able to read critically - with practice. But he doesn't have much time (Beatty and the authorities will find out if he has books sooner than later, and will come to burn them). So, Montag concludes that he needs a crash course in critical thinking/reading; he needs a teacher. He recalls meeting Faber and decides that Faber is the teacher who can help him.
A sieve is typically a mesh tool (wire or steel) used to separate solids from liquids. A sieve is used to pan for gold, separating gold and other minerals, allowing the water to pass through. Montag recalls his cousin daring him to use a sieve to collect sand. The sand is fine so, like water, it passes right through, thus making it impossible to be retained in the sieve. This is the feeling Montag has when he reads. He can not retain any significant knowledge. His mind is like a sieve; the words and ideas just pass on through. He needs a teacher to help him structure his thinking in order to retain the knowledge of what he reads. Until he gets Faber's help, the best thing he can do is memorize what he reads:
But he read and the words fell through, and he thought, in a few hours, there will be Beatty, and here will be me handing this over, so no phrase must escape me, each line must be memorized.