Decide what type of music that you want to train your voice to sing. Although many of the learning tools are the same across all genres of singing, you'll be better able to monitor your progress when you know the type of music you're performing.
Work on breathing and maintaining breath control. Though an unconscious act in daily life, breathing is an active part of the singing process. Expanding the lungs is an important part of developing control over breath. As an exercise, take a large breath of air (shoulders relaxed, don't tense up) and release the breath slowly in a quiet hiss. Maintain the hiss for as long as possible. Time yourself and try to improve by several seconds the next time.
Perform exercises that work the middle and comfortable range in your voice. These exercises can be found online or in a singing theory book. The middle range is different for all singers. To find it, sing a familiar song to determine the pitch you choose. These are the comfortable notes in your range. As an example exercise, pick a note in that comfortable range and sing it on several vowels. Try to morph from one vowel on that note and make the vowels sound even—do not move your lips too much in changing vowels.
Practice singing a familiar song quietly as well as loudly. Just because a song is quiet doesn't mean it requires less breath control; on the contrary, air must be moderated even more with quiet singing. When singing quietly, avoid introducing a whispery or airy quality into the voice. When singing loudly, think more about control rather than pure volume.
Work to expand your range. As an example exercise, sing a pitch from your middle range on an open vowel ("ah" or "eh") then sing four pitches in the major scale above it, then back down, step by step, to the original note (so, if you're starting on A, sing: A, B, C sharp, D, E, then reverse those notes back down to A). After each round, move up a half step (C to C sharp, for example), until you no longer feel comfortable on the highest note. For the lower range, reverse the exercise by singing notes down a scale then back up, moving a half step downward each round. Using a keyboard during this exercise is helpful.