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The second active pair. Pi'el historically intensifies or makes a root transitive, but in modern Hebrew it is just as often the binyan a verb simply lives in, especially borrowed and invented verbs (טִלְפֵּן "phoned", מִחְזֵר "recycled"). Pu'al is its passive twin, which today shows up mostly as a "ready-made" adjective (מְפֻרְסָם famous, מְסֻדָּר arranged). The shapes are sharp and easy to spot.
Pi'el, three signposts, A dagesh doubles the middle root letter. Past mould _ִ_ֵּ_ (diber, limed, bikesh). Present mould מְ_ַ_ֵּ_ with a leading מ (medaber, mevakesh, melamed). The verbal noun is the very productive _ִי_וּ_ (dibur, tiyul, bikur), covered fully in M6.
Pu'al, the u that means "it was done", Pure passive of pi'el, marked by a u vowel: past _ֻ_ַּ_ (dubar, bukash), present מְ_ֻ_ָּ_ (medubar, mevukash). You will meet it most as an adjective: מְפֻרְסָם (famous = "made-famous"), מְתֻרְגָּם (translated), מְבֻקָּשׁ (in demand). See a מ + u shape → "something was done to it".
One root, two binyanim
From "X did the action" (pi'el) to "the action was done to it" (pu'al). The u vowel is the flip.
Pi'el, active
דִּבֵּר
diber, he spoke / talked
Pu'al, passive
מְדֻבָּר
medubar, (it is) spoken of / "we're talking about…"
Pi'el, active
בִּקֵּשׁ
bikesh, he requested / asked for
Pu'al, passive
מְבֻקָּשׁ
mevukash, wanted / in demand / sought-after
Pi'el, active
פִּרְסֵם
pirsem, he published / advertised
Pu'al, passive
מְפֻרְסָם
mefursam, famous / well-known (made-public)
דִּיבּוּר←ד ב ר+_ִי_וּ_
dibur = "speech / talking". Every pi'el verb has this action-noun: דיבור, טיול (a trip), ביקור (a visit), תיקון (a repair), סיפור (a story). Spot _i_u_ → it is a pi'el action-noun.
Pi'el: active verbs
Pu'al: passive, mostly as adjectives
Pi'el action-nouns ( _ִי_וּ_ )
The snowball: each pi'el verb hands you a noun for free.
Decode drill: read the shape
מְ + a-e vowels = pi'el present (active). מְ + u vowels = pu'al (passive / adjective). _i_u_ = the action-noun.