There are 3 main avenues where you can get trained in dog grooming. First of all, you can enroll in a professional groomer school and get a classroom based type of training. A second option is to go through some home study professional training or books to get the adequate training for a start.
You can also find a groomer who is willing to teach and get some training under him. One thing to note about training under professional groomers is that they are not easy to find since you will be a potential competitor to them in the future. They might not teach you all that they know due to this conflict of interest. Continue here to see the pros and cons of attending groomer school and using home study professional training.