Could I look up traditional lore from random correspondence tables I have access to that aren't really cited or sourced? Sure. That's not what I tend to do in my practice, though; I use my knowledge about the materials and work with it more directly.
Take copper. I ask what I know about copper (and if it's very little, I research it). Off the top of my head, I know that copper is an excellent conductor of electricity, which makes it a very appropriate component for a wand (which is mostly used to direct energy). Do the same thing with the agate. In terms of the chemical structure (SiO2, or silicon dioxide), an agate has the same composition as quartz does. It comes in all colors of the rainbow, and are typically created within volcanic rocks. Agates have a high hardness, no cleavage, tend to be waxy in luster, fracture with sharp edges. A variety of correspondences can come from that, but in general, it speaks Earth of Earth off the cuff to me. Then there's the wood. Oak trees are associated with lightning in various folklore, and IIRC, there is scientific evidence that they are struck by lightning more often than other genus groups. From this, I can link the tree to anything that lightning represents to me, such as inspiration and misfortune, but also to protection (because its propensity for being struck means other trees are saved). Q. rubra also tends to grow on uplands and slopes, giving it a sort of 'elevated' status. Q. rubra and similar canopy oaks in the woodlands around my state are "keystone" species in those forest communities, meaning they support lots of other wildlife and define an ecosystem. Thus, I could link them to prosperity and stability, Earth Element qualities.
All the above is what I mean when I said "know your materials" in the summary earlier. If you know the materials, the methods write themselves. It's like cooking. If you know what garlic does, you can use it in any recipe with ease (provided you also know some cooking techniques). You can read books about food, learn from other chefs, and at some point, you've just got to chop some garlic yourself.
Mmm... garlic...