You can follow two general paths to become a winemaker: you can either try to make your own wine at home while learning as much as possible about the winemaking process — this will give you the skills necessary to build a business or get hired to a larger winery — or you can try to get a job at a winery and learn the skills necessary to become a winemaker. No set education level is necessary, and you do not need to obtain any degrees or certificates, but you will need to educate yourself on the winemaking process and become an expert on wines in general.
If you choose to look for a job at a winery, you should expect to start with a job that is quite far from the actual winemaking process. You may end up harvesting grapes, operating a bottling machine, or even operating a forklift, but this is a crucial step if you want to become a winemaker: not only does such a job allow you to become known by the winery owners and managers, but you will also be able to glean valuable information on the winemaking process and perhaps even become an apprentice to the current winemaker.
Starting to make your own wine at home is a great way to learn more about the process, but to become a winemaker on a larger scale, you will need to turn that hobby into a serious pursuit. This will mean an investment of time, effort, and money; starting a winery from scratch is an exceptionally expensive endeavor, and very few winemakers pursue this path. Starting out at home will give you a foundation for winemaking, and it will give you the confidence to pursue a job at a winery. Don't expect your small operation to grow, however, without a significant investment of time and money.
You can take courses that will give you some of the skills and knowledge to become a winemaker. These courses may be offered at a winery, at a community college, or by an independent winemaker. Learning as much as possible about the winemaking process will make you a more valuable candidate for a job at a winery or a vineyard. This can set you on the path toward becoming a winemaker down the road, but be prepared to invest many years to learning as much as possible about the process and about the wines being produced.