Change is always difficult, and it is especially difficult for infants and small children because there is no ability to understand the need for the change. The best way to change is with a change in routine, as well as constantly reminding and constant watching over of your son. While weaning him on to milk is a necessity, it will not stop the behavior towards wanting your breast. Your son (if he doesn't already) will "get" what no means, and when he tries to pull at your shirt much less get to your breast, explain to him, very simply, that it is not ok. He will not understand that it is inappropriate for him to do that, but he will understand a very simple "no, that's not allowed." He will come to find out that he is only allowed to have your breast when you say it is the right time. With vigilance and consistancy, it won't be long until he stops that behavior.
At the same time, or after, what you can do is pump some breastmilk (if you can...I had enough for 3 kids after I had my son, but I couldn't pump more than a drop) and mix that in with whole milk (I know, yuck, but it is the best thing for him right now). Start cutting back on his nursing times once every few weeks or month (whatever you can do...start in the middle of the day and work yourself out ending with the nighttime ones, keep him busy, he won't notice) and during the day when it is not time to nurse, he only gets milk (mixed w/breastmilk or not), water or a small amount of watered down juice and he only gets it in a sippy cup. Since he already knows how to use his sippy cup, it shouldn't be too much to ask. When he "asks" for a drink, or it is time, let him choose. You can have water or milk. At dinner time, he can only have milk to drink or he can have nothing. Sounds harsh, but it'll be OK. Giving him the choice will help him to decided among the "most gross." Being that he is one, you will have to do something like hold one in each hand and let him point and then switch hands and ask again. Children this age do have some preferences and some will actually choose the same stuff both times. You may have to set a cup of both in front of him and let him go for whichever he wants. Like I said, he won't go thirsty for very long.
Take care,
M. M.