How should one pray if they missed two rak'ahs with the imam in a four-rak'ah prayer, especially concerning making up the beginning of the prayer in terms of recitation and the end of it in terms of tashahhud, and what is meant by that?

The latecomer (masbuq) makes up for what he missed of the recitation and builds upon the rest. So, making up (qada’) applies to what was missed before joining the Imam at the beginning of his prayer, and building upon (bina’) applies to what he caught up with the Imam at the beginning of his prayer. What is meant by "sayings" is recitation specifically. As for other matters, he builds upon them, such as actions. So, if he missed two rak'ahs from a four-rak'ah prayer, he performs them and recites Al-Fatiha and a surah.