The following series of short exercises should help you become more familiar with the sounds that can be derived from the major scale. Each of them uses the syllables do, re, mi, fa, so, la, ti, and do again. These are called sol-fa syllables.
They are useful for becoming familiar with all the pitches of a major scale, and their positions in relation to the foundation note of the scale (do). The sol-fa syllables are also useful for practicing many of the basic sounds used in singing.
As you sing each of these exercises, remain as relaxed as possible and sing with an open flowing sound. Keep your posture straight and focus your voice straight ahead as if you were singing into a microphone at a comfortable height.
Do not "reach" for any of the notes as they get higher or lower, but simply allow the sounds to come out naturally. You may not be able to sing these exercises easily to begin with. Be patient and practice them regularly, but only for short periods of time at each session. There are three ways to learn these exercises.
Now try some short melodies using sol-fa syllables. They contain syncopated rhythms created by the use of rests and ties. If you have trouble keeping accurate time while you are singing, try clapping the rhythms while counting the beats out loud and tapping your foot. This is a great way to practice any rhythm you have trouble with.