Firstly, this is about one month of your life and a goal that is very reachable, the only thing on your way of learning to sing (maybe not well, but acceptably) is YOU.
YOU NEED TO COMMIT TO THIS.
All the material you will need is available free online. So, seriously, all it demands of you is that you do the work! You don't need to do it well, you just need to do it. Even if you are making fun of it, it will work!
Learn the basics. Yes, you can learn them in a day. The thing with learning to sing is that you learn the basics very quickly, and then you just train and practice and drill, day in and day out. *sigh*
- pose, posture
- warming up, scales
There's dozens of videos online about these things. Go and find them. I am not a voice coach or a professional singer. I'm just an enthusiastic amateur. :-D
How to take care of your voice
There are things you should never do and things you should always do.
That information is also readily available online.
One thing important is to learn relaxation.
Lung capacity! Take care of your asthmatic problems if you have any. Get in a good physical condition. It helps, too. Learn to hold breath under water.
Create yourself a schedule.
Building the voice
- expanding the range - so find your vocal range on day 1 and see how much you have expanded it on day 30 :-)
- getting more secure, pitch practice, tone etc.
- technique practice, like how to use falsetto, how to do runs and riffs, how to scat, how to scream etc.
- getting more power to singing, belting
- being able to hold a note, sustain a long note
- expressing the emotions
Try to give singing at least half an hour every day.
You need to sing every day. The more you sing, the better you sing.
But it is better to sing warm-up exercises, scales, general singing exercises, exercises designed to solve specific problems you have, exercises designed for each area of singing and building the voice.
All this is freely online, you just might need to search a little.
Here's some additional help:
How to Learn to Sing
John Quinlan and Frank Sinatra: Tips of Popular Singing (Vocal Calisthenics)
how Frank Sinatra learned to sing
30 day singing challenge
There is no anything special you must do for each day, you need to EXPRESS THE WORD OF THE DAY IN YOUR OWN WAY. Any which way you choose is good and right.