To begin getting comfortable with alternate picking, I would suggest practicing on just one note; down-up-down-up-down-up, until the picking hand is comfortable with the motion. Then, add another note, playing each note 8 times (alternating 4 downstrokes with 4 upstrokes), until you're able to switch seamlessly between the notes. Eventually, the alternate picking motion becomes second nature, with the hand alternating up- and downstrokes automatically.