This root means being firm, steady, reliable, and from that one idea two whole families branch out. On one side: faith and trust. To believe is to treat something as firm; אֱמוּנָה is faith, אֵמוּן is trust, and אָמֵן (amen) literally affirms "it is firm, so be it". On the other side: mastery and craft. The one who has made their hand reliable is אֻמָּן the craftsman or אָמָּן the artist, and to make a body reliable through repetition is לְאַמֵּן, to train. Faith and skill turn out to be the same word: both are firmness you can lean 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.
Two senses split cleanly across the binyanim. The hif'il לְהַאֲמִין means "to believe" (to hold something firm), while the pi'el לְאַמֵּן and its reflexive hitpa'el לְהִתְאַמֵּן carry the training sense: the coach makes the athlete firm (pi'el), the athlete makes themselves firm (hitpa'el). The plain pa'al and the passives are not lexicalized here as everyday verbs.
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.