You are already taking the first step. You are reading the answer to the question.
There are many ways to approach this, however, we think you have to simply get started. Hopefully you will get the "bug" (wine bug that is) and graduate to higher levels of learning and enjoying. Keep in mind, if you do not enjoy it .. you'll never go any further. Enjoying it could be the pleasure of drinking/tasting of the wine or the satisfaction of the learning about it (or any combination of the two).
The fact that you realize that you'll probably not like all wine, but appreciate learning about it, bodes well for you to stick with it and continue to increase your level of interest and knowledge.
Later we'll talk about referred and preferred learning materials whether they be books or schools or events, but for now, to capture your attention, let's just do a simple trial. Two whites and two reds. For this trial you do not need to spend a lot of money. You do need to get four wines with differences just to show yourself that there are differences.
Feel free to ask your local wine shop or store that has someone with at least some knowledge of wines, for their opinion or suggestion. Explain that you are starting to learn and want two different tasting whites and two different tasting reds. You may even go as far as simply asking for a dry red and white and a sweet red and white. That alone will show you a side by side that not all whites are the same or reds (how often do people simply ask whether you want white or red?).
If you shop and no one is around and you have to pick for yourself for reds why not go with a Lambrusco and a Cabernet Franc (or Sauvignon) and compare. With whites make it a Moscato and a Sauvignon Blanc. Distinct enough for you to "get the point" and get started.
The key though is at the beginning, not to go into this expecting to like the wines, but more to start learning about them and begin the process of recognizing differences. we may spread out some of the tips .. however, more to follow ..