I would recommend taking a class - an appreciation for wine class is a good place to start. At first you'll learn about wine itself but in most of those classes there will be winemaking portions.

There are also tons of great books out there that you could read. I don't have any specific book recommendations, I would just find one that is interesting to you and start there.

Going on winery tours is a great way to learn about wine and wine making in an interactive atmosphere. You'll see and hear a lot of things that will give you a basic feel of how it's done, especially if you visit during harvest, which I recommend.

During harvest a lot of wineries are looking for help and you can get what's called a 'harvest job'. You'll get to do a lot during harvest with no experience. They'll throw you right into the middle of it. You might get laid off at the end of harvest but if you go back the second year they'll hire you back because they know you know what you're doing. If you do that a couple of times, they see you're interested and a lot of times you can parley the experience of a couple harvests into an actual winery job.