Firstly, you'll need to find a recipe.
They look like a regular item with a scroll/paper under them:


They drop like ordinary items, can be found in chests or as drops.

Next locate the crafting shroomite in the tavern, he's right above the bartender here:


After talking to him you'll be presented with the crafting screen, clicking a recipe will preview the result:

Next click the "inspect" button on the left side of the screen, this will give full details of the item to be crafted as well as show you the material requirements:
Materials are obtained from chests while playing or as rewards for completing a map, you can clearly see which materials you have on the right-side of the crafting menu.

Finally, click the "craft" icon at the bottom of the inspect page:

The item will immediately be placed into your item box, a single use of the recipe will be used up in the process, how many uses a recipe has is indicated by a blue number on the upper-left corner of the blueprint's icon.

Materials

From the crafting menu, left-click a material to prepare it for packaging, a yellow number will appear next to it to indicate how many you want to make tradable, you can select multiple types of materials in one go, right-clicking reduces the amount you want to trade.
In this picture I have a single material selected and I'm trading 1 of them:

once you're selected your materials, click "Store parts in crafting parts box" at the bottom of the menu.

The parts box is now in your item box, ready to trade:
You can now trade it like normal items or send it your your Playverse account for trading via the steam marketplace / trade systems. (not yet available at the time of writing, this is a confirmed bug the devs are working on)

To unpack a crafting box you received in a trade or you no longer want to trade, select it in your item box and click "use" (or press "u" on the keyboard).

Gold

To trade gold, follow the above steps, but instead of clicking materials to pack select the amount of gold at the lower-right corner, then click "store coins in coin pouch", it will add a coin pouch to your item box which is used in the same way as a materials box.