The best way to significantly improve your singing is to allow yourself the freedom to just relax. If you tense up, get nervous or over think it, these feelings ultimately affect how you actually sound. You cannot properly relax your mouth, throat, shoulders and stomach if you are stressed, worried or anxious.
Once you have blocked everything else out and you feel your body relax, you need to focus on your posture. You want the breath to flow freely out through your mouth. If you slouch your shoulders over or tuck your head in, you are disrupting your breath in a negative way. You may find yourself tense back up again when you start focusing on your posture. If this happens, start over again and concentrate on the relaxation. It will all come together eventually with a little practice.
Learning how to properly breathe can make all the difference in the world in your sound. Do you find yourself getting winded or not being able to hold that last note? That all has to do with breathing. Chances are, if you run out of breath or cannot control your voice, you are breathing from your chest. This may sound like the logical thing to do if you are new to singing but what you really want to learn to do is breathe from your diaphragm. This muscle is so much stronger than those in your chest so when you learn to use it properly, you will be quite surprised at just how much air you have leftover. It may feel awkward at first but with practice, it will become natural.
It is also crucial that you thoroughly warm up before singing. Skipping out on your warm up makes your practice session somewhat worthless. If your voice is not warmed up, it cannot possibly be used to its full potential. In fact, you do more harm than good because without a warm up, you can easily injure your voice. Humming, singing scales and reciting tongue twisters are all excellent vocal exercises to engage it when you have a goal of improving singing.