The score is read by the conductor. All notes played by all instruments are in the score.
Let's illustrate with Joe Paparone's arrangement of The Barber of Seville Overture.
Time reads from left to right.
“The
Barber of Seville Overture” by Rossini
Arranged by Joe Paparone 1998
Concert Score excerpt
This is a concert score.
The key signature is the same for each instrument.
Each instrument is written to its key.
There is no difference in sound between the concert and transposed scores. In the concert score the focus is on concert pitch, the universal sound. In the transposed score the focus is on the language of the player, the parts are written as the player reads them.
“The Barber of Seville Overture” by Rossini
Arranged by Joe Paparone 1998
Transposed Score excerpt

“The
Barber of Seville Overture” by Rossini
Arranged by Joe Paparone 1998
Concert Score excerpt
Many woodwind instruments are transposing.
Bb clarinet is transposed up a tone.
You must be careful of the clef. Clarinetists read treble clef. It is bad form to give them music in any other clef. So Bb bass clarinet is transposed up a tone for the key and an octave for the clef.
“The Barber of Seville Overture” by
Rossini
Arranged by Joe Paparone 1998
Transposed Score excerpt

The string instruments in this syllabus are non transposing: harp, violin, viola, cello and double bass. Concert and transposed scores for these string instruments are the same.
Contrabass (double bass) is a special case. Contrabass is a deep instrument, so deep its best sounding range is well under the bass clef. We write contrabass an octave higher than it sounds so it may be read comfortably on the bass clef. When contrabass and celli read the same note they sound an octave apart. Have a listen to the MIDI files.
“The
Barber of Seville Overture” by Rossini
Arranged by Joe Paparone 1998
Concert / Transposed Score excerpt
Following is the piano keyboard and its relation to the treble and bass clefs. It is easy to see from this diagram how many notes at the heights and depths of music are not covered by the clefs.

Some instruments are naturally very high or very low. The glockenspiel pitch is much higher than the treble clef. It is written on the treble clef, two octaves under its actual sound. Electric bass and contrabass are deeper than the bass clef. They are written an octave higher than they sound.
You may like to browse our Musical Instruments Reference.
This appears to be a concert score. Looks can be deceptive.
French horn is written in the concert key signature but not in the concert key. In this score French horn notes are transposed a diatonic 5th higher than concert without changing the key signature.

For now the tasks involved in understanding a score may seem incredibly complex, but in time you will get a feel for the instrument's keys and pitch.
Being able to tell whether notes are concert or transposed, irregardless of the key signature, is something you will pick up as you learn about chords, progressions and other music theory fundamentals.
"Become an arranger first, then an orchestrator, and then a composer." - Joe Paparone

Joe Paparone is an Australian music arranger of the highest international calibre. Allow him to share 35 years of real world experiences with you.