The easiest way is to simply sing. I know you think you are not making progress but you probably are much better than you were. You seem to pay attention to what is going on so that is good to.
Make sure you sing in the proper range. If you are singing to high or low you will struggle. Don't try to sing something you can't because you simply won't get better(and likely will get worse).
Pitch is about control. You develop control from exercising and it takes time(like any activity). If you think you are singing in tune but not, then maybe you don't know what you are actually doing. You should be able to diagnose this easily. Sing single pitch with a single pitch from another instrument. If you are out of pitch here but you think you were in pitch then you need to ask yourself what really is going on. Are you actually out of pitch or do you lack control and waver so that it sounds bad(e.g., pitchy)?
Make sure to work on vibrato... it can work wonders for getting on in pitch(for many reasons).
- The mouth is a resonator and your vowels are basically different enhancements of different frequencies. When you sing, you have to be critically aware of how your mouth is shaped because it will effect the pitch you are singing in an indirect way. There is a lot of theory about it but just experiment. Usually things like ee's sharpen the perceived pitch while oo's flatten. This is why sometimes singers sound a little strange is that they modify their vocal resonances to help increase their pitch slightly. They might even say a word "wrong"/"weird" just so they can hit the note.
Again, by practicing this you will start to see how it works. Hold a pitch and just move the mouth in different configurations and you'll quickly learn how it works. If you pay attention you'll notice there are sweet spots. Some people can control it so well they can create overtones and multiple notes(some can even sing "harmonies" this way... check out youtube for some Russian chick that is amazing at this... It's called overtone singing)
- Resonance is, as you probably know, when a sound reinforces itself and creates positive feedback. This happens when the instrument(your vocal track and body) are in the correct configuration. Since you are unique, your configuration is different than everyone else and part of singing is learning these "sweet spots" because they give you the most "power" for the least effort.
e.g., suppose you are pushing someone on a swing. If you are smart and want to do the least amount of work you push the person just as they reach the peak and go with the flow(push to hard to quick and you ruin the "resonance").
Singing is similar. You have to learn to control all these different factors and it takes time and proper practice(paying attention). Some things will just have to develop over time as it takes strength.
So, for a minimum of 1hr a day, you must do the following:
Warm up(body, mind, and throat) = physical exercises. This, of course, is not necessary, but will help you quicker as it gets you ready and helps prevent injury or strain which simply slows you down.
Do vocal warm up exercises. This is humming, lip trills, etc. This help get the throat ready for singing and starts building control and strength with minimal stress. This will make further practice more effective so it shouldn't be skipped.
Practice your arps and scales. (play a chord and sing the chord tones, play a different chord, etc)
Have fun! Make up songs, etc. This can be fun and since you are doing it on your own you don't have to be self conscious. Just do it. You may suck at first but you'll get better and it's more fun than just doing 3 alone. (basically add lyrics to 3 and sing the tones in different orders, etc)
Sing others song... make sure you find songs you can seem to sing best. Don't get anything that is close to being outside your range. You are not here to prove anything.
Realize it will take time... don't stress out, it will happen with practice, it is probably already happening and any day you might have a breakthrough.
Don't worry too much about how good you are(that seems to be your problem). You suck, just accept it, that is the first step to recovery. Accept it may take 20 years for you to become a good singer. Ok, you said you sucked, but obviously you are about how good you are(it is a conscious thing).... this is the bane of becoming good though.
Think about it this way: You are a good singer, but you are just in a long warmup process. the warmup process takes about a year or 2 or 3 or 4. But once you warm up, you'll be awesome. (that is how it works and is analogous to warming up for practice)
You need to get any negativity out of your mind because it truly does prevent you from being successful... sometimes we even do it intentionally. If you have a fear of someone hearing you sing, then you have a problem with being self-conscious, not singing. When you get over the self-consciousness of it(specially if you are older, children rarely have this problem because they are so oblivious to how much they suck), you will be able to actually sing. I went through a similar process. Living around other people, being late to singing, and not wanting being to "know" how bad I suck(well, how bad I thought I sucked) preventing me from actually trying to sing. Once I just sucked it up and said "I don't give a shit what people think, I am going to do this for me... screw them if they don't like it" I almost immediately improved 10x(or whatever number you want, kinda meaningless).
Our minds are our biggest enemies. Singing is actually relatively easy once you let all the crap that makes it hard go and just sing. Why? Because to sing you have to actually make a loud noise where people can hear you... and if you have issues with that you tend to sing soft and it is relatively impossible to sing properly soft.
Proof? Think of a wind or brass instrument. If you do not put enough wind in to them they won't make a good tone! Your vocal track is simply a brass or wind instrument... no different. You have to give it good "support". Flutes, for example, will have pitch changes depending on how hard you blow. If you blow soft they tend to be flat and too hard will make them sharp. You can correct this with lip angle and other methods... singing is similar.
The good news is that all the above doesn't matter. If you simply start singing to enjoy it you will learn it just as you learned anything else in your life easily(usually the things you wanted to learn). Don't play mental games and don't fall for the games of other people and you will be success. Again, singing is truly not hard and you will realize it one day and say "WTF! THIS IS EASY!". I'm not saying it doesn't require work, I'm saying that the problems you think you have are not issues, the issue is something else... solve that problem and everything else will fall in to place. The reason why you can't sing is because you are doing it wrong... stop doing it wrong ;)