Memorizing the first 10 to 40 elements of the periodic table can be achieved through various methods. Some users suggest repeatedly reviewing a periodic table, with resources like webelements.com being recommended for their clarity. Flashcards are also highlighted as an effective tool for memorization. A user shared a mnemonic they created, stringing together the first 10 element abbreviations into a memorable phrase. Additionally, there is a reference to a related thread discussing techniques, particularly one by a user named Chroot, which is noted for its effectiveness. Overall, consistent study and creative mnemonic devices are emphasized as key strategies for learning the elements.