Hire a vocal instructor or singing coach. This is the most effective way to learn to sing, at least in the beginning. You may abandon your singing coach once you have some of the basics under your belt, but a complete beginner should have a teacher if possible. A professional singing instructor can show you exercises and teach you techniques it could take you a long time to learn on your own.
Focus on breathing technique at first. A lot of beginning singers sing from the throat, not from the diaphragm. Singing from the diaphragm is your goal. Try breathing in through your nose rather than through your mouth. This makes it easier to fill your diaphragm with air. Compare the two methods and feel the difference. Getting air into your diaphragm will not only help you sing with more power, it will prevent you from the damage you can cause singing from your throat.
Learn to sing scales. You can purchase a book of vocal exercises or find them online at no charge (see Resources). Singing scales may seem boring at first, but scale singing is an effective way to train your ear to hear pitch. As you sing scales, try singing the same scale in different octaves, meaning you will finish the scale and repeat the same scale one octave higher. This helps you determine and increase your singing range.
Practice enunciation as you work on vocal exercises. Singing vowels help exercise your vocal chords and improve your singing clarity. When you sing vowels to a scale, practice singing the notes consecutively and out of order. Constantly singing scales in note order will not help you work on vocal runs (and control of your voice), and it won't help you achieve the ability to make vocal leaps (moving from one note to a much higher or lower note).
Sing along with some of your favorite songs and record yourself. Sometimes you can't hear the off-key singing while you're singing, but listening back to the mistakes become obvious. Singing along with your favorite artists, as well as artists who challenge you vocally, is a good way to measure your progress.