Here is *one* method for someone without much theory background who wants to begin composing in C major, as you asked. I'm not saying it's the best or that you'll stick with it, but it may help you get started.
1. Sit at the piano and play the C scale to get the C sound in your mind. Relax, put your fingers down and start noodling around (with your right hand) until you come up with something you like. You might want to start on C, E, or G and you will probably want to end on C.
2. Play it again, until you know you can play it consistently. Try to jot it down on manuscript paper.
3. Now to add chords: Every note of the C scale *may* be harmonized by one of these chords (there are many other chords available, but these three are the biggies that are good to start with): C major (I) (C E G) , F major (IV) (F A C), G major (V) (G B D). So, supposing you have an A in the melody; the most likely chord to go with it is F major, because it has an A in the chord.
Note that the note C may be harmonized with either a C or an F chord, and G may be harmonized with either C or G chords.
Write the possible chords above the notes on your manuscript paper. Now try adding the chords while you play the melody.
4. A few notes about chords:
a. you don't necessarily need a chord for every note. Make sure the long notes are harmonized.
b. the most satisfactory finish will be a G chord followed by a C chord (this is called a V-I progression, and in Western music it says, "the end").
c. you will *probably* find the F chord to be used the least of the three.
d. if none of the three basic chords sounds right, try something else -- D minor (D F A) or A minor (A C E) for instance.
e. it is not necessary always to harmonize a note with a chord that contains the note. You might find that you like the sound when you play an A in the melody with a C chord in the left hand, for example.
f. the G chord is more commonly followed by the C chord than by the F chord.
g. chords can be inverted to make them easier to play. Very commonly, the C chord will be played in root position (C E G), the F chord in 2nd inversion (C F A), and the G chord in 1st inversion (B D G). When played like this you can progress smoothly from one to the next.
As I say, this is one way to get started...hope that helps.