Practice singing arpeggio runs. An arpeggio is the notes of a chord sung separately, or broken. The notes of a C major chord consist of the first, third and fifth notes of a C scale. A C arpeggio would be these notes sung individually. Try adding another C, higher than your starting C, on top of the run; sing this arpeggio both in ascending and descending patterns. Since you aren't singing the scale notes consecutively, but jumping to each note in the arpeggio, you're working on the muscles that help make a smooth transition between notes that aren't side by side. If you don't know what these notes sound like, use a piano or other instrument to play them, then match what you hear. You can do major arpeggios in any key by singing the first, third and fifth notes of the corresponding scale. By singing a flatted third instead of a third, you can practice minor arpeggios, which will exercise your vocal cords differently.
Sing a scale introducing the staccato technique. Use the syllables "do-re-mi-fa-sol-la-ti-do." This will require you to sing the notes in short bursts, using your vocal cords to snap the notes off as quickly as you sing them. Combine the staccato technique by alternating longer notes with shorter ones. This exercise effectively strengthens your vocal cords' ability to control the notes you sing.
Blow air from your mouth without pursing your lips to do it; this is called a "lip trill." You will feel your lips vibrate. Control the air flow with your diaphragm, not with your throat. If you find yourself having trouble blowing air out of your mouth without pursing your lips, press the tips of your fingers against your cheeks and push in, then release the pressure. Do this until you can produce what sounds like a motorboat as you blow air from your mouth. When you can do this, try singing notes in this fashion.
Use an "ah" sound to sing scales, concentrating on making a smooth transition between the notes. Start with the first five notes of any scale. Sing these notes ascending and descending until you move between them without a break. When you can do this, try starting on the last two notes of the scale, singing the same exercise all the way down to the first note of the scale.
Use vocal training software, such as "My Vocal Warm-Ups." This software works like a karaoke tape. The exercises appear onscreen in musical notation. You can sing along with the exercises and watch the notes you sing on your screen. The software gives you starting pitches and allows you to set your tempo. It features a variety of major, minor and pentatonic scale exercises, as well as arpeggio exercises.