Basically, turn on Collector's Glove and go to gather the item to bring up the new Collectable window. You'll then use Methodical Appraisal until you get to 30/30 Wear or 240+ Rarity (the minimum for the two starting items to be accepted as a turn-in). Then you just click collect until the node runs dry as per normal. There's more to it than that since you have other skills to make the rarity-increasing process easier (e.g., Discerning Eye lets you spend GP to increase your next Appraisal's strength). Personally, I just think of it like crafting? You increase the quality of the item through various actions and are limited by the item durability.
So, if you're doing Mining and getting Yellow Copper Ore, you'd most likely want to come in with 500+ GP. Turn on Collector's Glove, hit the node, use Toil, hit Yellow Copper Ore, use Discerning Eye + Methodical Appraisal, Methodical Appraisal, Collect / Use Methodical Appraisal if not at 240+ Rarity, Collect, Collect, Collect, node runs out of HP.