Sing lots of scale exercises at the very top and bottom of your vocal range. Notice which notes you typically sing in your chest, or lower, voice and which you sing in your head, or high, voice. You'll find that there are a few notes in between that you have a difficult time identifying.
Identify your vocal break or bridge. These are the notes you have a difficult time singing clearly and comfortably in chest or head voice. This range will be at the heart of developing your mixed or middle voice.
Experiment with different vocal exercises singing the notes in your break or bridge range. Try each note on different vowel sounds like "ah" "oh" "ee" and "oo." Take note of the vowel sounds that create easy and natural placement for these notes.
Vocalize with the vowel sounds that created natural placement and resonance in your break or bridge zone. Find your middle voice by gradually moving the notes in the lower end of the range up and out of the chest and more into the mask of your face. For the higher notes in the break range, focus on moving their placement from the head voice to the front of the mouth. Placement of the middle voice is key to creating good resonance.
Add words to the sounds you are creating and eventually incorporate them into full melodies. It will take a lot of practice to find your middle voice and to know which notes in a song you should sing in the mixed voice. Eventually, you may find that you begin to use your middle or mixed voice so often that the transition between chest, middle and head voices becomes seamless.