It is difficult to do so in a short text, but still, I will say few things that hopefully will help:
Some people start reading saint Theresa of Avila with this book (“The Interior Castle”). It is true, this is her “Masterpiece”, but this doesn't mean that we can understand her right away. My suggestion would be (if the person is only starting to read saint Theresa) to read the book of her “Life” written by herself. Then the "Way of Perfection", then "The Interior Castle". It takes more time to do it this way, true, but maybe it is easier, more fruitful and more faithful to her thought and to the chronological process of her thought. “The Interior Castle” ("Castillo interior" or "Las Moradas") is a work of maturity (1577).
Some other persons would start by reading an introduction to her thoughts, to her terminology (the words she uses).
Some would prefer to read a Biography of Theresa of Avila. We have various good ones (Marcelle Auclair, Ephren de la Madre de Dios-Otger Steggink)
Her thought is not systematic, even if the book of the Interior Castle looks systematic.
One advice thought while reading any of her books. While reading, try to see:
1- What God wants to do in the Soul (in general and in yours in particular): His goal, his aim. The holy project of God for you.
2- What are the advices saint Theresa gives in order to know what to do in order to grow. The obstacles to avoid (temptations, sins, bad habits, …), the acts to do, the virtues to grow (with the grace of God),...
3- What will happen if I do what I have to do (at the stage where I am): description of the action of the Grace of God in us, the transformation that it provokes. What you feel, what you experiment.
So one can read the book once, just to have a general idea. Then, re-read it again, with a pen and a notebook handy, writing down, for each stage, the 3 points mentioned above.
While reading the Interior Castle, the "temptation" is to try to know where we are in the journey, if we are at the first, second, third, forth, fifth mansion,... If we are motivated by the true desire to know what we are supposed to do in order to grow, this means that our conscience is pure, and that we will make a good use of this knowledge (knowing were we are are). We will focus on the useful advice given to us by saint Theresa, at our stage.
Another advice to the reader who reads for the first time: take what God gives you, what speaks to you (regardless of where you are in the journey). One can do a kind of revision to what could be lacking.
Remember that a normal “fervent Christian” or “charismatic person” (a person that belongs to the charismatic movement in the Church) already crossed the border between the third and the fourth mansion (entering what Theresa calls the “supernatural” that doesn’t depend on us, or the "specific help of the Grace of God"). So, please let us not spend all our life reading the first 3 mansions. Let us go rather swiftly through these first 3 mansions and focus a lot on the Fourth and the Fifth.
The majority of fervent people (charismatic certainly) are in these two mansions. The art would be to practise with constancy the advices given in these two mansions, especially the fourth, so the will becomes rooted in God, and one reaches the fifth mansions. (fourth are like climbing and the fifth are like being stable in a “state” (the “Union of will”).)
Mind you, after that, God starts to "talk" to us differently. Here we need the help of saint John of the Cross and the description of the deep purification of the spirit (the upper part of the soul). Saint Theresa of Avila doesn't really mention it in an obvious way, while it is important. (See how Father Marie Eugene in his book "I want to see God", intended to be a comment to her book "The Interior Castle", did add the description of the deep purification of the spirit explained by saint John of the Cross. They in fact complement each other.)
This change of behaviour of God toward us is in fact fundamental. We need to know it. This is why saint John of the Cross writes his books at the first place. He sees beautiful and fervent souls who reach that point (end of the fifth mansions) and stop their growth, and the reason is that while God is changing His behaviour with us, the change is perceived as a “regression” (going backward in the spiritual journey). Because one perceives that God is far, against us, and all the "milk" we used to get disappeared.
I hope this helps.