A great way to get started finger-picking, and train your ears to the sound of the open strings, is this four-note roll. Using the thumb, index and middle fingers of your picking hand (T-I-M), you are going to simply pick the notes in the order of their pitches from lowest to highest (C-E-G-A).
Start with the thumb on the open 3rd string C. Next pick the 2nd string E with your index finger. Pick the 4th string G with your thumb and finally the 1st string A with your middle finger. Do this very slowly and train the muscle memory of the fingers to this T-I-T-M pattern. Hum the notes as you play them. You may also try to sing the solfege or do-re-mi syllables as you practice. Once you have the roll under your fingers and in your ears, practice it in even time (1 & 2 & 3 & 4 &) putting the emphasis on the 1 and the 3 beats. After practicing this for a while, you should be able to put the roll on automatic pilot.