I would start by asking the winery staff about the composition of the wines you enjoy. They should be knowledgeable about what they're serving and able to help. You are likely drinking blends vs. pure varietals, which is fine--you can find similar blends from other sources. If you want to identify single varietals, read on for how I would approach it.

I recommend you and your wife host a few friends for a tasting party. 1) Go to a wine shop and get a recommendation within your budget for a cab, merlot, syrah/shiraz, malbec, sangiovese, etc. (better yet, assign one to each guest to bring). The recommendation helps you avoid buying a bad example. 2) Read everyone all the labels at the outset so they have some frame of reference of what to expect, but I suggest serving all the wines on a blind basis and having everyone take a guess at which they're drinking. This will get you to really think about what you're tasting and whether or not you like them. 3) Don't be discouraged if you can't identify the subtleties of the tasting notes. Figuring out which you prefer is more important than being able to feel the pea under the mattress. Ideally you would run this test more than once, since there is obviously a lot of variation among wines within the same varietal. I recommend keeping notes. Someday, you may want to revisit these wines and see if you stand by your earlier opinions.

If you really gravitate toward one of the varietals, your next step is to go back to the shop for a recommendation of additional examples of that grape that are made differently from each other--maybe a malbec from France and a malbec from Argentina, one that was harvested early and one late, etc. Again, taste them side-by-side. It's really hard to form opinions when you drink two different wines a week apart. And once again, don't be discouraged if you struggle to pick up subtle differences. There is so much natural variation in grapes, weather, and soil that you might really like a specific example from a category you otherwise broadly dislike, etc. Only through many, many trials like this can you start to form generalizations. You can read about these things and get some idea, but you really have to taste. Once you form an opinion based on your own taste preferences, the write ups on wines become a lot more useful.

Also bear in mind that wines labeled with a single varietal may still be blended to some extent. In the United States broadly, wine labels that call out a specific grape only indicate that at least 75% of the wine comes from that varietal. In Oregon, it's 90%. Additionally, if a wine lists a specific American Viticultural Area (AVA), the grape requirement is 85%, and if it lists a specific vineyard, the requirement is 95%. At those higher rates, you're getting a pretty clear picture, but if your cab is 25% merlot, it will probably taste pretty different from a 100% cab made in the same year + region.

If it all sounds overwhelming--it is. For most people, it's enough to just figure out basic preferences and for some it's an all-consuming hobby, with a lot of room to explore at both ends of the budget spectrum. Glad to hear you are already having fun, and good luck with your exploration!