NotePlayMusicSpeed and loudness are different instructions
Tempo is how quickly beats pass. Allegro asks for a quick, lively tempo; it does not mean loud or necessarily happy. Dynamics describe loudness. A written p (piano) asks for quiet playing, while f (forte) asks for loud playing.
These instructions can happen together. A passage may be quick and quiet, or quick and loud. Read the word and the dynamic separately before deciding how to play.
One speed, two dynamic levels
Keep the quick beat. Begin quietly at p and play loudly from f; the dynamic change does not change the metronome rate.
The music says Allegro and p. Which instruction should you follow?
A crescendo takes time
A crescendo (often shortened to cresc.) asks you to get gradually louder across a phrase. An opening hairpin under the notes gives the same direction. It does not mean start suddenly loud, and it does not mean speed up.
In the example, begin at p. Grow louder across the marked notes and arrive at f. The written notes and beat stay the same while the loudness changes.
From quiet to loud
Do not jump to loudness on the first note: let the sound grow through the hairpin.
A phrase begins at p and has an opening hairpin ending at f. What happens?
Count the pulse named by a metronome mark
A metronome mark has a note value and a number. The note value tells you which duration is counted as one pulse; the number tells you how many of those pulses fit in a minute. A crotchet = 120 mark means 120 crotchet pulses per minute.
If the symbol is a quaver instead, quaver = 60 means 60 quaver pulses per minute. Do not silently change the quavers into crotchets: the symbol is part of the instruction.
Read both parts of the marking
The note symbol sets the crotchet pulse; the number says 120 such pulses in one minute.