If you play the c-major scale on a keyboard, which are all white keys played beginning at c, you get c → do, d → re, e → mi, f → fa, g → sol, a → la, b → ti. Analyzing the intervals you find a half tone step between mi and fa and between ti and do. The position of these semitones within the scale gives it its characteristic.
Solmization introduces a relative tone system whereas generally we work with an absolute one. In an absolute system, each note refers to a specific frequency. For example: a’ → 440Hz. In a relative system, the relation between the notes is more important. In “do re mi fa sol la ti do“ the relation between each note is determined, but the frequency for do is variable. It is like a ruler that you can lay down on different places to see where your sol is, when your do is a at this or that note.
Exercise 1: Play a singable note on your preferred instrument and sing the major scale on the syllables do re mi fa sol la ti do ti la sol fa mi re do up and down. In the beginning, you can play along with your instrument as you sing. Practicing this exercise you will get used to the syllables, their order and their sound within the scale. You also learn to think relatively which is a very important ability as you sing more complicated songs.
Exercise 2: You can do this exercise alone or with a partner. Take your left hand and look at your fingers. Each finger and each flap of skin between your finger stands for a syllable (see illustration). Pinky → do; Space between pinky and ring finger → re, ring finger → mi …. Define the absolute note of a syllable by the help of a tuning fork or an instrument. Now tap with your right index finger on a random finger or flap of skin between two fingers and sing the corresponding syllable with the correct pitch relative to the defined note. Vary your initial defined anchor note from time to time. Practice until you are able to find the correct notes at decent speed. If you have practiced alone until now ask, someone else to tap his fingers for you as it is more challenging