Poor breath control is probably a big part of your problem. The first step in breath control is making sure you're breathing from the diaphragm. What this basically means is that you should expand around your middle but your chest shouldn't move.
An exercise to help make sure you're doing this right is to stand up straight and hold a pencil horizontally between your sternum and a wall. Start by breathing deeply, and then sing some. You'll be able to tell pretty quickly if you're breathing right because the pencil will push you back or you'll drop it. Even if you already know how to breathe, you should always keep it in mind while you're practicing.
Also, try to breathe deeper than you think you need to when you sing. If you've ever inflated a balloon and then pinched the sides of the opening to make that squeaky noise, you might have noticed how it starts off high pitch and consistent in tone and then gets lower in pitch and more uneven in its sound. This is a good representation of what happens when you sing. The more air you have in your lungs, the easier it will be to push it out at a constant rate. It will feel weird to breathe that deeply at first, but makes a big difference.
To practice your both your breath and pitch control, I'd suggest singing a song you feel confident with veeeery sloooowly. Crescendo on each note, which is basically a fancy way of saying start each note in the song quietly and let the note grow louder as you hold it.
It will most likely sound silly, but this is a good exercise for two reasons. One is that it forces you to breathe deeper than you normally would. The other is that singing well when you're not confident in a note is almost impossible, and this lets you practice your breath and pitch control with a song you like and feel good about.
From there, it will mostly be a matter of practicing and having fun with it. Singing is just like any other instrument in that it takes a lot of talent to master, and you'll be much more likely to practice consistently if you have fun with it.