I just saw this on my mobile and had to jump on the computer.
There are historical reasons for most of this but just start with your C scale as a starting point (also easier because no sharps/flats).
The 7 tones you're referring to, that is a diatonic (dia = 7; tonic = tones). It is the most common scale pattern in Western music (also pentatonic, 5 tone scale, penta meaning 5).
Now in Western music, you have 12 total tonalities, each of which has an enharmonic equivalent (same note, different name; the name you use depends on the context).
C
C#/Db
D
D#/Eb
E
F
F#/GB
G/F
*
G#/Ab
A
A#/Bb
B
C
*(double sharp, rare to see this but goes back to historical technicalities)
Now scales are made up of how each of these tones relate to one another by interval degree.
C D E F G A B C
This is your C Major. The pattern of steps (one half step is two tones next to each other, C to C# for instance or E to F; whole step is two half steps) would be: w w h w w w h
The octave is the root. Now the scale patterns are useful but not as useful from a theoretic standpoint.
What we have then is intervals and their relationships. Of these, in Western music, diatonically based scales you have 4 perfect tones (1 4 5 8 [octave]) and 4 major tones (2 3 6 7). Lower case m = minor, upper case = Major, + = augmented, - = diminished (listed without enharmonic equivalents with the exception of augmented 4/diminished 5):
Root (P1)
2m
2M
3m
3M
P4
4+/5-
P5
6m
6M
7m
7M
Octave (P8)
The interval pattern is simply what it takes to map out, from the root, the major scale. P1, 2M, 3M, P4, P5, 6M, 7M, P8:
C (P1/Root)
C# (2m)
D (2M)
D# (3m)
E (3M)
F (P4)
F# (4+/5-)
G (P5)
G# (6m)
A (6M)
A# (7m)
B (7M)
C (P8)
Now the way intervals work is also what determines chord builds (must have root, third, fifth for a proper triad, typically [exceptions abound]).
Your sharps and flats essentially mean one half step up (for sharp) or down (for flat) from the given tone. So if you had to modulate, Writing an F note in the sheet music and flatting it would give you an E, but for theoretical purposes and playability via site reading and so on, you wouldn't write E, you'd write Fb (which also shows a modulation). Don't worry with modulations for now. Just explaining what sharp and flat means.
There are 12 fundamental tones in Western music which repeat. You don't really need to know much about frequency in most cases, just know that the frequency perfectly doubles when you go up one octave. If you place a C and then play the next octave of C (often written C' which is called C-prime), then the wavelengths perfect match to make them perfectly harmonious, though the C octave is twice as fast (perfectly twice as fast) and therefore is a higher pitch.
Now back to intervals.
Your intervals can be major or minor and your chords can be major or minor (M/m); they can also be diminished or augmented.
However the NOTES in the scale are NOT individually major or minor. A note by itself can only be natural (♮), sharp (♯) or flat (♭). These are called Accidentals. You usually won't see a natural unless you need to alter a note that, according to the key signature or modulation, is usually sharp or flat, as being natural.
OK so for something simple and highly relevant, writing out a scale and the enharmonic equivalents.
A Major, since that was mentioned. You only use each tone (C D E F G A B C) ONCE. Never use the same tone twice, that's what accidentals and enharmonic equivalents are for.
Correct: A, B, C#, D, E, F#, G#, A
Wrong: A, B, Db, D, E, Gb, Ab, A
This goes back to readability on the staff (sheet music). If you're going to learn theory, being able to read sheet music at least moderately is a MUST. It will get more and more imperative as you advance in theory to be able to read sheet music.
Going back to C major, you may see it listed by Roman numeral. These indicate the triad chords on each degree. For the major scale (regardless of tonal key being C or D or whatever, this is ALWAYS the major scale):
I ii iii IV V vi vii°
Capital numeral is major, lower case is minor and a lower case with a ° is diminished.
So to make a proper triad, as I said before, you need root, third and fifth. This is based on the actual root of the chord, not the root of the scale so for C major... (root of chord in bold at bottom):
G A B C D E F G
E F G A B C D E
C D E F G A B C
Now look at the first chord, CM (I). You have your root C P1, (d = second, skip), your third which is a Major third interval above the C and then your G is your fifth above C and it is perfect, so you have a major triad (R, 3M, P5).
Look at the second chord. You have your root of D, then the F is a minor third above the D (F# would be a Major third), and then your A is a perfect 5th of D so you have a minor triad (R, 3m, P5).
The last chord is diminished, the B because you have over the B, a minor third and a diminished 5th. (R, 3m, 5-). Look at the list of intervals above and map it out from the B: B is your root, then you have C 2m, C# 2M, D 3m, D# 3M, E P4, E# 4+ but because we already have an E in the key (C Major), it must be F which makes it 5-.