As a voice teacher, I've found certain exercises that work well for most singers and help get fast results. Unless noted, they can be used with any scale. But a word of caution: Don't take any of these exercises higher than is comfortable. You can listen to my podcasts at www.speechlevelpodcast.com for some examples.
1. Glides Through a Straw
Blow air through a small stirring straw while phonating glides up and down through your range. The backpressure created by the resistance of the straw presses down on the vocal cords and helps decrease puffiness, a major source of vocal trouble.
2. Lip Trills
This is a variation of the straw exercise. Gently blow air through closed lips, keeping them relaxed, and sing an uh vowel underneath. Your lips should start to trill. The resistance of the bubbling lips helps maintain cord closure, an important element of good singing.
3. Creaky Doors
This is a great exercise to help build the coordination needed to maintain proper cord closure. Make a little edgy sound, like a creaky door or a rusty gate opening. Do a scale on this sound using very little air. The idea is to not let the sound get breathy or squeezed.
Make the ng sound from the word hung. This sound is produced with the tongue and soft palate together. This again provides backpressure, while also making the transition between the lower and upper registers (chest voice and head voice) easier.
5. Nasty Nays
This is done using the word nay on a bratty or Wicked Witch–type sound. This exercise also assists in cord closure, while the exaggerated sound makes it easier to ascend into the upper register without cracking or flipping.
6. Hooty Gees
This is the opposite of the previous exercise, and it's quite useful for a singer experiencing excess tension. Using a dopey cartoon voice (think Yogi Bear), say the word gee. You should feel your larynx drop. The g consonant should also help with cord closure due to the backpressure it creates, so you can experience accessing the upper register with a stable larynx and closed cords. This coordination is extremely important in good, healthy singing. Once this exercise is comfortable, you can drop the dopey imposition and sing on a more natural sound.
7. Coo Coos
This exercise is great for working the upper register. The coo can be made to sound hooty, like an owl, for extra ease in working high notes.
This is very useful for singers who are weak or breathy in their lower register. The sound is on theaah of cat and can be exaggerated by sticking the tongue out slightly. Do this in your lower register in a five-tone scale (1–2–3–4–5 to 5–4–3–2–1 of the major scale). Use very little air, as you don't want any breathiness in the sound.
9. Googs and Mums
These are best used once the voice is experiencing proper cord closure and ease of production. The word goog (the vowel sounds like the oo in good) has both a hard consonant for cord closure and a vowel that will help stabilize the larynx. Be sure to maintain the vowel in the upper register, as vowel widening (gaag) can cause tension. The vowel and consonant of mum provide a bit less help thangoog, making this a slightly more advanced exercise.
Going from a more closed or narrow vowel to a wider one on a sustain is a great way to balance resonance. The more closed vowel will help you get into your upper register. Gradually open to the wider vowel while keeping the resonance in the same place. If the tone gets shouty or strained, go back to the narrow vowel to get the voice balanced again.