C# major is the plain C major scale with every single note nudged up by a half step. Same shape, same bright, settled sound, same family of chords, just sitting a little higher. The catch is on paper: all seven notes carry a sharp, and two of them have names that look strange the first time you see them. Once you see why, this key stops being intimidating and starts looking tidy.
Most people meet the major scale as C major: C, D, E, F, G, A, B. On a piano that's just the white keys, and if you sing it you get the familiar do, re, mi, fa, sol, la, ti, do.
That scale is built from a fixed pattern of steps. A half step is the smallest step in Western music, like moving from one piano key to the very next one, black or white. A whole step is two half steps. The major scale always follows this pattern:
W - W - H - W - W - W - H
Start that pattern on C and you land on the white keys. Start it one half step higher, on C#, and every note moves up by that same half step. The result is C# major:
C#, D#, E#, F#, G#, A#, B#
Nothing about the sound's character changes. It's still the reference major scale, the one every other mode gets compared to: bright, happy and resolved. You've simply moved the whole thing up one key on the piano.
Here's where newcomers usually pause. E# is the same piano key as F. B# is the same key as C. So why not just write F and C?
The rule is simple and friendly once you know it: a major scale uses each letter name exactly once. C, D, E, F, G, A, B, all seven, in order. If you wrote F instead of E#, you'd have F# and F in the same scale and no E at all, which makes the music much harder to read and the chords harder to spell. Calling it E# keeps every letter in its place.
The same goes for B#. It's the seventh note, so it needs the letter B. Spelling it C would leave you with two C's and no B.
So on the keyboard, C# major is five black keys (C#, D#, F#, G#, A#) plus two white ones, E# and B#. Play it slowly and watch your hand: it feels like a different scale from C major, but your ear will hear exactly the same pattern of steps.
C# major is actually the less common way to write this sound. Most musicians write it as Db major, which uses 5 flats instead of 7 sharps and sounds exactly the same. Same keys on the piano, same pitches for a singer. You'll see C# major in some classical music; Bach wrote a Prelude and Fugue in C# major in his Well-Tempered Clavier. Learning both names means you're never thrown when a chart picks one over the other.
The key signature is the set of sharps or flats written at the start of each line of sheet music, so you don't have to mark them on every note. C# major has 7 sharps, the most any standard key signature carries. Every line, every note: sharp.
Its relative minor is A# minor. Relative keys share the exact same notes and key signature; the minor one just treats A# as home instead of C#. Same seven notes, darker centre of gravity.
Every note in the scale matters, but two give major its personality. In this key they're F#, the 4th, and B#, the 7th.
The 7th is the big one. B# sits just a half step below C#, and that tiny gap creates a strong pull upward. Sing up the scale and stop on B#: you'll feel almost unable to leave it hanging. That pull is why melodies in major sound like they're heading home.
F# is the gentler counterpart. It sits a half step above E#, the 3rd, and tends to lean down onto it. In a melody, F# often feels like a soft sigh that settles into E#.
Stack every other note of the scale and you get its chords. A triad is three notes; a seventh chord adds a fourth on top. Here's the whole family:
Notice G#7 contains both B# and F#, the two character notes. That's why the V chord feels so eager to resolve to C#: B# rises to C#, F# drops to E#.
Try C# - A#m - F# - G#, then back to C#. It's the classic I-vi-IV-V pattern behind countless pop and doo-wop songs. For a jazzier flavour, play D#m7 - G#7 - C#maj7 and listen to how smoothly each chord slides into the next.
Your root note C# sits on the low E string at frets 9 and 21, and on the A string at frets 4 and 16. The 4th-fret A string root is the comfortable place to start: play C# there, then walk up the scale using the W-W-H-W-W-W-H pattern, counting two frets for a whole step and one for a half. Say each note name aloud as you go, E# and B# included. It feels fussy for a week, then it becomes second nature.
Hold a C# chord on any instrument, or have a drone playing. Sing or play up the scale and stop dead on B#. Wait three full seconds before you let it rise to C#. Then do the same with F#, letting it fall to E#. Those two small resolutions are the whole emotional engine of the major scale, in this key or any other.
For the bigger picture, read The Major Scale (Ionian Mode).