The mahAvAkyas are the 'great utterances' that appear in the Upanishads. The Wikipedia page on them gives a fairly accurate description.
https://en.wikipedia.org/wiki/Mahāvākyas
For the sincere aspirant, the following sequence might be useful. The mahAvAkyas are to be experienced directly by the sAdhaka. First, they are listened to from the Guru, or read. Then they are contemplated on. But in my experience, the experience of the mahAvAkyas is a deeply intuitive insight. It happens after the stage of dharma megha samAdhi which is described in the Yoga Sutra. From this intuitive flash of understanding, it became clear that the mahAvakyas are experienced in a logical sequence, which is:
brahman satyam jaganmithyA
prajnAnam brahma
ayam AtmA brahma
tat tvam asi
aham brahmAsmi
ekam advitIyam brahma
sarvam khalvidam brahma
For the beginning sAdhaka, it will be difficult to even contemplate or intellectually understand and grasp the first mahAvAkya. For this, the ignorant notion of reality informed by the senses into which the mind is so deeply sunk, first has to be shattered. Unless the mind sees the 'cracks in reality' that I have referred to elsewhere, even the faintest glimpse of the truth of the first mahAvAkya will not be perceived. Unfortunately, many people take psychoactive drugs to accomplish this. The Yoga Sutra itself notes the aushaDhi or herbs can induce samAdhi. However, I do not recommend this approach. There is too great a risk for the undisciplined mind to get addicted to this external crutch by which it attains an experience, which is also grounded in ignorance. The best way to gain experience is through the practice of HaTha and RAja yoga and by awakening kuNDalinI. The experiences following kuNDalinI awakening are very similar to those experienced by tAmasic fools who take ayahuasca, whose active ingredient is the drug DMT.
Another far superior alternative is to have shraddhA or faith in the Guru's words and practice sAdhanA diligently. That has the power to reveal the meaning of all the mahAvAkyas to the sincere aspirant.