Somewhere, I have read that we need to consume proteins to make amino acids to make new proteins. What does it suggest? How do we make proteins from proteins?
Essentially, yes, "proteins that we consume form new proteins that are different".
The processes are each of them topics for themselves. In short, consumed proteins are digested by peptidases (enzymes) in the stomach, breaking them down into their consituent amino acids. These are absorbed in the gut and transported in the blood to all cells. These take up amino acids and attach them to tRNA molecules which are used in translation to form new body proteins.
You ingest daily dietary protein which your body hydrolyzes to get all the building blocks for other proteins (amino acids).
Also, from diet you can get essential amino acids that cannot be synthesized de novo by the organism which is more economical than amino acid synthesis. Other amino acids can be constructed by metabolic processes.