Arpeggios are basically scale fragments and/or triads.
Typical arpeggio would be 1 - 3 - 5 (triad) or 1 - 3 - 5 - 7 (dom7 or maj7) or 1 - 3 - 4 - 5 (triad w/ sus4).
Say you take C major chord. It's made up of the notes C - E - G...that's 1st, 3rd and 5th notes from C major scale...C, E, and G...C major triad.
Play them over 2 octaves like this:
-------------------------------8-
--------------------5----8-------
---------------5------------------
------2---5----------------------
--3-------------------------------
-----------------------------------
That's a C major arpeggio over 2 octaves.
You can apply the same method using any combination of notes over any scale/chord to create an arpeggio.
