Do, Re, Mi, Fa, Sol, La, Ti, Do names the degrees of a major scale in movable-do solfege. Do follows the tonic, so you can sing the same relationships in any key.
The major scale's step pattern is 2–2–1–2–2–2–1. The half steps occur between Mi and Fa, and between Ti and the next Do.
Fixed-do traditions assign syllables to fixed note names instead. Guitarbacus's movable pattern is especially useful for thinking in relative intervals.
Pick up your guitar
Choose C Ionian and sing the first three notes before you play them. Then change the root to D and sing the same relationships.