Also known as the lawn mowwower by my three year old son.
Before I explain what you're going to do, I want to tell you why this works:
To sing you need to have a nice steady stream of air. The air makes the chords vibrate (SOURCE), the vibrations bounce around your mouth, throat and head (RESONANCE) or, to simplify further, you MAKE the sound then SHAPE the sound.
So let's start with MAKING the sound.
1) Creating a steady stream of airflow
I have a few favourite exercises for this (the straw, the lip trill and the blower) but this is today's top choice.
These exercise are my own - some are adapted from an ENT website because I find they work really well.
1) Yawn. Feel the throat open and the soft palate lift. Let that yawn out in a soft deep throated sigh. Hmm.Feel the lovely vibrations in the base of your throat, down your chest and into your sternum.
2) Now, around that lovely low note, make a strong sustained sssh sound with the vowel OR vocalised in your mouth (Say or then close your mouth in a ssh and continue the sound)
Feel the vibrations. Let them fill the resonating cavities around your eyes and cheeks, let them flood through your mouth and throat, down your chest and into your sternum. Make your self a vessel for sound and enjoy. Do this for as long as your like. It will be engaging your breathing muscles without you having to think about them (feel your stomach tighten as your make the noise). It will remind the muscles of the job they're about to do.
Look at your neck, it will be widening and relaxing as the muscles release despite the flow of sound.
Focus on your pharynx or mouth. The closure at the front will allow the sound waves to bounce back and support the chords so let are not straining to control the gush of air from the lungs.
Let your cheeks relax, maybe puffing out slightly
Let your jaw relax as if there is a nice open gap between your wisdom teeth.
Let your tongue hang. That beast can get tight and now is the time to let it loose.
Keep going until you literally feel warm: warm and buzzy, loose and ready.
Go as low as you comfortably can to let the larynx drop and relax. Watch it lower in a mirror.
After this you can take the same sound up and down, sliding smoothly making sure to keep the air flowing (you should always be able to hear a steady ssssh with this sound). Try to feel the vibrations everywhere as you move, keeping the chest resonance as you go high and the cheek bone resonance as your go low.
When I do this exercise, I feel a little like how I imagine a monk might feel. I could feel a little silly, making noises like my three year old son behind a "yawn mowmower" but just give in and enjoy the feeling of being a vessel for sound. Letting your instrument play through you. I promise it works.