I've helped a few people to learn how to sing (I wouldn't go as far as saying taught) and there are three things I recommend.
1) Start with your ears.
Your ears are your most important tool when singing. You use them to help you pitch correctly, to make sure you're singing with the rest of music and to evaluate how you sound. I'm not sure where you are so I don't know what specifically to recommend but there are plenty of exercises out there if you want them (these can start as simply as using a guitar tuner to make sure you're singing the right note). If you don't want to do exercises then I'd say simply pay particular attention to how you sound, get familiar with what it sounds like when you're bang on the note and when you aren't quite there.
It's very natural to tense up when you're singing, especially when pushing yourself. For me it is usually around the jaw, throat and shoulders. This makes singing tyring and strangles the sound. I don't have any specific advice here other than be aware of it and try to release the tension. Stance is quite important for this, plant both feet on the ground and make sure you are balanced and comfortable.
3) Focus on Breathing
Cliche... but true. Everyone knows you want to be breathing 'from your diaphragm'... this just means is that you want to use your stomach muscles to control your breathing rather than your chest, because that gives you a lot more power and control. Again, there are millions of exercises but to keep it simple I suggest this: actively push your stomach out when you breath in and actively pull it back in when you breath out. At first these will be two things that you happen to be doing at the same time but over time the muscle memory will come and you will find that the stomach starts controlling the breathing. What I particularly like about this is that it is something you can actively do. So much singing advise (like points 1 and 2) is pretty abstract (relax... listen...) and can be hard to consciously start doing... but 'stick your stomach out' is nice and direct, something you can grab onto on day one.
(Side note, try not to lift your shoulders while breathing in, this adds tension and doesn't give you as much air).
Beyond those things my main piece of advice is... sing, just sing.
Like any muscle, the more you use your voice the strong it will become and the more familiar you will be with how to use it.