Hi
You question is very complex to answer. There are many ways to build chords.
Ok, I'll give it short and sweet...
Major scale of C is
CDEFGABC the 1 is C the 3 is E and the 5 is G.
Ok, you COULD use this knowledge that C is made up of CEG to understand what order the notes are in.
Let me shed some light on something you may not know. In chord theory there is what is called INVERSIONS. So what is an INVERTED chord? Its one where a note other than the root (1) is in the bass.
a Chord is said to be in FIRST INVERSION when the 3 is in the bass and a chord is said to be in SECOND INVERSION when the 5 is in the bass.
So a C chord with an E in the bass is still a c chord but it is in first inversion. Chords that have more notes can be in 4th or more inversion, but the farther away from the root (1) you get the more unstable the chord usually sounds.
Many folk/bluegrass/country players use inverted chords to get that alternating bass note going. For instance if you take an Open C Chord finger the "normal" way, and then use your pinky up on the Low E string (the fat one) at the third fret (G note), you've just created on Open C chord in third inversion and this chord is used alot to alternate between the c note on the 5th string and the G on the 6th while struming the chord.
Another way to know what order the notes are in is to use the
planetalk method.
Hope this helps... constructing chords, IMHO, is ONE OF THE MOST USEFUL, ENLIGHTENING AND PRODUCES A MORE KNOWLEDGABLE PLAYER than many other endeavors. I suggest you get a chart that shows the tones that make up a particular chord and build them ALL from scratch. This is easily done using planetalk. I suggest you memorize all the chord formulas (tones).. know that a major is 1 3 and 5, minor 1 flat 3 and 5... etc...
good luck.
Brian