When you purchase regular (non-pressure treated) lumber, consider it dry enough to work with for any household construction project.
When you purchase pressure treated lumber, expect it to feel damp to the touch. You may want to allow it to re-dry for 3-4 months before using it to avoid the majority of the warping/twisting/shrinking effects of drying lumber. You can, if you desire, purchase a moisture content meter to ensure the wood has dried back to your desired moisture content, if you feel the exact moisture content is critical to your project.
When designing and building your project, plan for some amount of seasonal wood movement. Know that the vast majority of expansion will be in width (the 4" dimension of a 2x4), a bit of it will be in the thickness (the 2" dimension of that 2x4), but almost none in the length (not enough to ever really be concerned about).
The long story:
As I covered in the answer I linked to in my comment on your OP, wood is a natural product and will expand and contract seasonally. When you build with wood, whether for an outdoor project like a pergola (as you've asked) or a solid plank door (as was addressed in the linked question), or an indoor project like a solid wood dining room table, dresser, or decorative storage cabinet, you must allow for this expansion and contraction or your project will end up warping and splitting. (And it might do one or both, even if you allow for it in construction.)
"Wet" v "dry" wood has very little to do with droplets on the surface, it's all about the moisture content on a cellular level within the board itself.
When a tree is cut down, it is "green" or "wet" wood - each individual cell has a very high moisture content because it was (just moments ago) a living thing that needed that moisture to survive. Immediately after being harvested, the cells begin to lose their moisture, this is a process called drying. As others have discussed, it takes about 1 year per inch of thickness for boards to dry out to the point where they're "stable". While they're drying, the wood can warp, twist, split and crack, which is why you see so many pieces of wood at the local home center that look more like the keel of a boat than they do framing lumber.
All the wood you buy at your local home center will be dried lumber. The lumber mill will have stored it for roughly 12-18 months to allow it to dry. Before they ship it on, they will test for moisture content as Lee Sam noted in his answer and mark it as such. When you buy it, you can be confident that you're buying "dry" wood, though the moisture content may be higher or lower (by a couple of percent) than when it left the sawmill, depending on where the mill is, where you're buying it, the season it left the mill and the season you're buying it. It will be more "wet" in the summer, and it will be more "dry" in the winter, but again, only by a couple of percent, and this is well within the expectation for "dry" lumber.
If you were to go to a sawmill/lumber yard you could, if you desired, buy green lumber. You would only do so if you had a specific task in mind for working with green lumber (some people turn with green cuts, then let the warping become part of the look of bowl), or if you wanted to save some money by spending your own time & storage space to allow it to dry before using.