Rule 1: 1. مُجَرَّد and مَزِيد فِيهِ
A verb that consists of the three radicals alone is called اَلْفِعْلُ الْمُجَرَّدُ the bare verb: دَرَسَ, كَتَبَ, جَمَعَ. A verb to which one, two or three letters have been added is اَلْفِعْلُ الْمَزِيدُ فِيهِ the verb with an increase: دَرَّسَ (the middle radical doubled), كَاتَبَ (an alif inserted), اِجْتَمَعَ (a hamzat al-waṣl and a ت added), اِسْتَعْمَلَ (three letters, ا س ت, added). The added letters never change the root; they change what the root means.
دَرَسَ الطَّالِبُ الدَّرْسَ.
darasa ṭ-ṭālibu d-darsa
The student studied the lesson.
مُجَرَّد: the three radicals only.
دَرَّسَ الْمُعَلِّمُ الدَّرْسَ.
darrasa l-muʿallimu d-darsa
The teacher taught the lesson.
مَزِيد: one letter added, the doubled ر. To teach is to make someone study.
كَاتَبَ أَخِي صَدِيقَهُ فِي الْيَمَنِ.
kātaba akhī ṣadīqahu fi l-yamani
My brother corresponded with his friend in Yemen.
An alif after the first radical: the action is directed at someone.
اِجْتَمَعَ التَّلَامِيذُ فِي الْمَكْتَبَةِ.
ijtamaʿa t-talāmīdhu fi l-maktabati
The pupils gathered in the library.
Two letters added to جَمَعَ 'to gather (something)': the subject gathers itself.
اِسْتَعْمَلَ التِّلْمِيذُ الْمِسْطَرَةَ.
istaʿmala t-tilmīdhu l-misṭarata
The pupil used the ruler.
Three letters added to عَمِلَ 'to work': to put something to work.