OK, this isn’t quite a beginner’s tip, but it’s a great hack for remembering key signatures, relative majors/minors and chord relationships.
The cycle of 5ths, or circle of 5ths if you prefer, is a list of all the major keys and their relative minors, ordered by their key signature. For convenience it’s usually written as a circle rather than a long, endless line. The keys are represented by chord names. A letter by itself is a major key or chord and a letter followed by “m” is a minor key or chord.
The pattern is centred around C major and A minor, which have no sharps or flats. Reading clockwise, you progress further into sharps. Reading anticlockwise, you progress “backwards”, further into flats.
At the bottom there is an overlap where two possible note names can be used to describe the same root note. The trade-off here between naming these keys as sharps keys or flats keys is minimal. In actual usage, the choice may become clearer when considering the natural (easily played) keys of the instrument(s) chosen to play the piece and what other keys are visited within the piece.
in theory, you could continue in either direction, beyond 7 sharps or 7 flats, but then you’re doubling up with much simpler key signatures for the same sounding key so you would need a very good reason to go beyond 7.
For a piece in a given key, say A major, the most closely related keys and the primary chords are found immediately to the left and right of the home key, and their relative minors or majors inside or outside the purple line.. In the case of A major that’s A, D, E, F#m, Bm and C#m.
Note: in most gentes, the chord on the next key (the dominant) is played as a major chord, even if the home key is minor. For example, for A minor, the chords are Am, Dm, E (rather than Em), C, F and G.
Primary school students are usually taught the sequence of letters as a mnemonic – at my school it was “Go Down And Enter By Fifths”, with a C at each end. It’s boring and it’s technically incorrect (the pattern goes up in fifths the way it reads, not down). I’m sure you could make up a better one…
The Cycle of 5ths is explained in more detail in 12. Major Keys And The Cycle/Circle Of Fifths.