Three consonants carry one idea: adding, putting more onto what is already there. This root opens with a I-yod that hides in the modern verb: the archaic pa'al יוֹסֵף ("he will add / continue") is also the name Yosef, Rachel named him hoping God would add her another son. The everyday verb today is the hif'il "to add". From the same letters come the addition itself and the extra portion tacked on. Every word here is verified against pealim, niqqud included.
The same root runs through the verb system. Each binyan is a voice: it bends the one idea into active, passive, causative or reciprocal. Tap to hear.
This is a I-yod / pe-yod root, so the yod disappears in conjugation: the hif'il lehosif shows an וֹ where the root yod once stood. The pa'al יוֹסֵף survives mainly as a name and in elevated register; modern speech reaches for the hif'il. The nif'al is the passive: something gets added to a set. Pi'el, pu'al and huf'al are not lexicalized for this root.
Same root letters, different noun moulds (mishkalim). The mould tells you the function: who does it, the act of doing it, or the thing produced.
Strip the prefixes, suffixes and vowels. Three consonants remain, and the meaning lives there.