Read the script several times. The character is born out of that material and you will need to familiarize yourself with that material.
Record notes in the script detailing how certain lines or actions make you, as the character, feel. Even if you don't agree with them.
Write a short biography of the character based on your intuition and the material at hand.
With this bio absorbed, reread the script and write new notes detailing how you feel with this new backstory.
Compare both sets of notes. You may find that you didn't fully understood the character upon first reading the script, but now have a good grasp.
Ask the director for his/her vision and notes. Share yours. You both need to be on the same page.
Whether it is having people call you by the character's name or beginning to incorporate those quirks into your everyday life, do what you can to immerse yourself in the life of that character. These subtle actions truly help.