Andrew, I don't believe anyone can teach you how to sing. You have to teach yourself - the same way that you learned how to eat and speak and walk. You have to find your singing voice and then develop it – just like you found your balance on two legs and then learned how to run. Also you cannot be shy about it - it won’t work if you are.
The best way to sing is to try and try often, in 5 to 10 minutes bursts. The shower or bathroom is a fun place to make singing sounds and listen to them because it is very resonant.
All singing is produced on vowel sounds. Consonants don't have pitch. Some consonants like M and N are produced through a pitched hum - but that is not exactly singing. You need to work on what goes on in singing vowel sounds with your body.
Take a breath, think of a word like "who", "where", or "whah", say it out aloud and don't allow the vowel sound to finish. Keep the sound going (or resonating) for as long as possible - even after the count of one second you will be singing.
Try to extend the sound. Imagine the sound stretching or streaming out into the next room. How long can you sustain the sound? Notice that your stomach starts to tighten a bit - that is your diaphragm muscle kicking in to support the sound. Aim for holding the vowel sound for as long as possible while staying relaxed. Count in seconds in your head and keep a record of your progress.
Once you get the hang of extending the vowel sound focus on listening to the qualities of it - eg. volume (can you produce loud or soft?); pitch range (can you make the sound high or low?); pitch constancy (can you hold one pitch? Can you visit other pitches in the same breath?)
In addition to noticing your diaphragm move, think about your jaw, lips, tongue, cheeks and upper palate. Are they relaxed? What size and shape is the cavity inside your mouth? What happens to the sound if you change it? Make very small changes to consider the effects. Does it please you?
Next consider your nose, eyes, eyebrows, face, head and neck. Where are these positioned? Do they move? Are they relaxed? What happens if you raise your eyebrows? Close your eyes? Imagine your head has an invisible string lifting you straight up. Does it make a difference?
Move on to thinking about the rest of your body. Where are your shoulders, back, arms, bottom, hips, legs and feet? All these body parts have an effect on your sound. Experiment by moving these body parts differently. What happens?
Pay attention to your emotions too. Do you feel happy? relaxed? tense? anxious? angry? Ultimately singing should make you feel positive - in either a happy, envigorated or relaxed kind of way. If you don't feel uplifted, keep trying different body moves.
After you get a feel for your voice on single pitches or notes apply your knowledge to any song you know. Think about the vowel sound of every word sung and aim for the loveliest version of each one that you can muster. Sing a line at a time. Consider how you attack each word – particularly at the start of a phrase. Try to hit the opening note in the middle of its sweet spot. Also explore what it is to swoop up or down to a note - not always desirable but sometimes interesting.
Practice, Practice Practice - every day.
And enjoy it.
When you feel confident, join a community choir.
Learning to read music is also helpful, as is learning to play a pitched instrument like piano or recorder.