The Gameplay
This page explains how players actually use Reforges in-game: opening the menu, reforging an item, applying reforge stones, and how the cost scales. By the end you'll understand the loop your players see, so you can decide how to price and gate it.
Opening the reforge menu
Players run /reforge, or interact with an NPC that runs /reforges open <player>, to open the menu:

The glass on the side turns green when a valid item sits in the left slot, and the anvil shows status messages as you go. The whole menu is customisable in Plugin Config.
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Reforging an item
Place the item to reforge in the left slot. The right slot is for reforge stones.
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The glass turns green to confirm the item is valid. By default reforgable items say so in their lore, which you can turn off in config:
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An item that can't be reforged shows an error instead of turning the glass green:
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Click the anvil to reforge. If the player can afford it, the reforge applies with a chat message and a sound:

Reforge stones
Reforge stones apply specific reforges that the random roll can't give, so they're how you hand out your strongest modifiers. To use one, place the stone in the right slot and the item to reforge on the left, then click the anvil as normal:
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You build stones, and set a per-stone price, in How to Make a Reforge.
Reforge cost
Each reforge costs money, set by reforge.price in config. Reforging the same item repeatedly gets more expensive: the price is multiplied by cost-exponent (default 1.15) raised to the number of times that item has been reforged. Tune both in Plugin Config.
Where to go next
Make a reforge: define your own modifiers in How to Make a Reforge.
Customise the menu: change the GUI, sounds, and prices in Plugin Config.
Commands: see what you can run in Commands and Permissions.