The most fundamental aspect of learning to sing is to match pitch. Matching pitch involves two different skills: having an aural sense of pitch and being able to physically reproduce pitches with your vocal chords.
If you don't have an aural sense of pitch, chances are good you already know this. You may not be able to hear the difference between pitches, or perhaps someone in your life has already told you that you are tone-deaf in response to listening to you try to sing pitches. If this is the case, learning to sing will first require you develop a sense of pitch matching. One of the best ways to do this is by getting a friend with good singing skills to sing and hold pitches while you attempt to match them. Your friend will be able to tell you when you are successful, and, as you repeat this exercise, eventually you will learn to hear the difference for yourself.
If you already have the aural ability to hear the difference between matched and unmatched pitches, but lack the physical ability to match sounds with your vocal chords, all that is needed is practice. Use a musical instrument such as a piano or purchase a pitch-producing tuner or pitch pipe. Play pitches, then match them with your vocal chords. At first, this process will be slow as you learn where notes lie in the muscles of your larynx, but over time you will learn to hear a pitch and quickly reproduce it.
Once you have gained the ability to hear pitches and quickly match them with your vocal chords, the next step is to learn to produce sounds with good tone quality and a healthy use of your vocal chords. This requires learning how to breathe deeply and use large quantities of air while singing, how to use your vocal chord muscles in the most relaxed manner possible and how best to make the tone resonate in your throat and oral cavity.
While individual practice remains vital, and it is possible to improve these skills on your own, the best ways to learn these skills involve consulting a skilled vocal teacher. This is often necessary because only a teacher can assess what you're doing and correct mistakes you are unlikely to be aware of on your own.
As important as physical technique is, you must learn artistic style to turn technique into music. The best way to learn style as a singer is to listen to, imitate and take inspiration from other singers, especially those you consider to be great artists. A teacher can also help you develop your singing style by suggesting areas that need improvement or skills that you should develop, such as range and vibrato.