How will I know if my chanting is bringing me closer to Krishna? How long does it take to become Krishna conscious?
You can see that the chanting is helping you come closer to the Supreme when you see that your mind and senses are coming under control. When you see that you are less attracted to material things, or less frequently hankering and lamenting over material success or failure, then you can know that the chanting is bringing you closer to Krishna. Gradually you will develop a taste for chanting. You will long for the time and a peaceful place to chant His Name. You'll come to feel His presence and aspire to engage in his service.
How long this takes is up to you. How carefully you follow the process, what you eat, who you associate with, what you do when you're not chanting, will all affect how quickly you can perceive success. For example, let's say you have a disease. Your doctor gives you a diet, some medicine, and tells you to do some exercise. If you take the medicine now and again, ignore the exercise and diet, and wonder, "how fast will I get well?" the answer is "probably not very fast." You have to do it all to really be cured. So the time frame is in your hands.
Seek out good association, good opportunities to read and study the sastra (scriptures), good service, avoid eating tamasic and rajasic foods (foods in the modes of passion and ignorance), eat only prasad (food offered to Krishna), chant your rounds in the morning in a good place, free from distractions. All this things will maximize the speed of the effect. Good luck!
All the best!