Proper breathing is essential to good tone production and projection---it is the backbone of good singing. When practicing breathing, work on taking a relaxed breath (your throat should feel the same way it does when you're breathing out hot air to try to fog up a window) and inhale deeply, allowing the air to fill your lungs from the very bottom---your upper chest should not move. This approximates the natural breathing that happens when one is speaking, so this is a good thing to "practice" by observing what your breathing feels like they next time you're having a long-winded conversation.
Another aspect of breathing that you can practice is expanding your lung capacity. A good way to do this is to take a piece of paper (or start with a facial tissue, if you have difficulty) and see how long you can hold it against the wall with the force of exhaled air. As you improve, make the exercise harder by moving farther away from the wall.
Relaxation is important to good singing. Any tension you're experiencing will inhibit your breathing and create a strained sound, especially if you're tense in your vocal chords. Practice relaxation by learning body awareness; do a progressive relaxation (relax every area of your body, one part at a time) before you start your practice session, then periodically do it again during your session. Notice how much tension returns to your body between relaxation breaks and work on reducing how much of this tightness creeps up while you sing.
Practice relaxation of your vocal chords by paying attention to how your throat feels while you're singing. If you feel any ache or soreness, you need to reduce tension; singing should feel breathy and relaxed. Make gentle, sighing noises and work on making your throat feel this way during singing.
Intonation is as much a matter of training the ear as it is a matter of training the muscles of the voice. If intonation is a problem area for you, purchase a tuner with a microphone and pitch gauge that will tell you when you're matching pitch consistently. Practice with this device; when you first start, spend a lot of time watching the dial and holding your pitch in place, then work on looking away from the gauge and only checking back occasionally to see if you've stayed on pitch.
Another good way to practice pitch is to sing a capella (by yourself) in a practice area with a well-tuned piano. Play the first pitch of a song on the piano to match it, then sing through a passage and play the passage's ending note to see how close you've stayed to remaining on key. This will give you a sense of whether you tend to ride sharp or flat and allow you to compensate for the problem. Practice until you can sing through entire songs without losing pitch center.
Good tone in singing is often a matter of style, since different styles of vocal music will demand different qualities and colors of tone. All singing, however, requires a relaxed, supported approach in order to be healthy for your voice, so once you've mastered these basics of tone production, the best way to work on getting the particular sound you want is to listen to singers you wish to emulate and sing along. Experiment with altering the shape of your oral cavity; this involves the muscles in the back of your throat, so if you're not used to moving these around and knowing what they feel like, practice saying different vowel and notice the difference in physical feeling. Change your oral cavity while you sing and record the results. Listen back to see which ones sound the way you want them to.