Crafting Magic Items

The entire world is suffused with magic--but some substances and patterns are better at holding it than others. When a mage casts a spell, they accumulate energy from a power source, form it into a spell matrix (a complex pattern that directs and limits the magic so it produces a specific effect), then release it. But spell matrices are inherently unstable. To make magic last, it needs something that will endure, a vessel that will contain the power without dissipating and focus it to a specific effect. This is why Magical Items are so important. They allow a mage's work to persist beyond the flickering intensity of a single spell.

Student Crafting

As a student at the academy, your access to expensive materials is limited. While the caretakers give you everything you need to survive and thrive, they're not going to furnish you with gold, rubies and saffron if it isn't directly related to one of your classes.
Assume that you can make any Common magic item if you have the skillset, have taken the classes, and have the downtime.
For Uncommon items, you usually won't be able to get the necessary materials unless it's directly connected to a class
Students won't usually be able to make Rare or rarer items on their own/on the daily.

For examples of what constitute Common, Uncommon, Rare, Very Rare and Legendary magic items, see the 5e SRD: Magic Items

1. Materials
2. Construction
3. Enchanting

MATERIALS

Some materials are better at containing magical power than others. Gemstones are excellent resevoirs of magical energy, which is why they're used in so many items. Precious metals are valued for their ability to contain or channel magical power, leading to gold, silver, platinum and others appearing in magic items.
Many supernatural creatures contain inherent magical energy, or have properties that make them good resevoirs or conduits of magic. Dragons in particular are brimming with magic, so dragon's blood is used to infuse or quench weapons & items, dragon scales make excellent hard materials, dragon bones, and so forth. Among the Dragon Tribes this usually only applies to organic matter willingly contributed by dragons--voluntarily shed blood or scales, for the most part.
For organic matter, some trees have specific occult properties, specific flowers and plants have specific properties. Exotic materials are often rare and prized for their magical qualities.
It's worth noting that it's not enough to just make something expensive. Different materials and substances have different affinities. Fire Opals and Rubies are good for Fire Magic, for example, but rubies are also good for blood magic. Yew wood is associated with death and spiritual energy. There are so many different magical affinities, detailing them is far beyond the scope of this simple document. Think about what you want to create, what kind of materials would normally be used to create it, and which of those materials you could swap out for something with an affinity for the type of magic you're using (and how you're going to use it).
Also of note--the substance you use matters as much as the manner in which it is harvested. A branch of yew wood is decent for a wand. A branch of yew wood taken at midnight from a tree in a graveyard is better. Iron is fine, iron from the mountains where The Destroyer slew Erecura will be VERY DIFFERENT. Consider special circumstances of harvesting, special techniques, symbolic meanings in your materials as well as mere substance.

CRAFTING

In addition to using special materials, the procedures by which you create the item matter. There's a reason you see witches and spellcasters churning the cauldron thrice widdershins (counter-clockwise) and chanting. If they were just cooking up a tasty stew those steps wouldn't matter, but just like casting a spell involves verbal, somatic and material components, creating a long-lasting (or permanent) spell matrix--enchanting an item--takes specific steps from the start to the finish. Your crafting space must be isolated from unwanted magical interference. Your techniques must be carefully planned, each blow of a hammer or each woven stitch modifying not only the physical structure of the object, but the magical matrix you're creating and imbuing into it. Special catalysts may be introduced during this time--a sword might be quenched in dragon's blood or a magical oil. A cloak may be dusted with ground gemstone or pixie dust. A scroll would use expensive magical inks and only be written from the hours of 1am--3am every night for a specific spell.
To further solidify the magic, you may expose your item to powerful sources of energy (like a volcano, a natural lightning bolt, the light of the rising sun over the Mountains of Morning in the Sky Kingdom), or perform specific rituals (Draw blood from the left hand of three mages born in the fall, shatter an earthen vessel filled with snow collected from the highest mountain in the world, blessed by four warriors of impugnable honor). The problem with this sort of crafting is that while spells are formulas passed down from one mage to another, the SYMBOLIC magic of creating a magic item is far less well documented. Some items have specific recipes you can follow (often potions and scrolls fall into this category) but if you're creating something unique, you'll have to come up with this on your own.
Finally, patterns. This item needs to be a physical spell matrix, after all. The same patterns that help in spellcasting--magic circles, sigils, runes, and more--should be incorporated into the design of the object. You may inlay it with runes, filligree magic words, wrap it with a braid whose knots resemble the hand gestures used to cast a relevant spell. All these and more can help turn the entire object into a three dimensional spell matrix.

ENCHANTING

Really, the enchanting process begins at the very beginning when you're selecting your materials, and depending on the type of item it's usually not performed at the end as an afterthought, but throughout the entire crafting process. At certain steps you may focus magical energy on the object, casting specific spells into specific runes or aspects of the object. But at the very end, it's common to cast multiple spells over the item and "seal" the magic within, with both magic and a symbolic act, such as quenching a blade as a spell is cast upon it, adding a final ingredient and bottling a potion, sealing a scroll with wax and completing the spell to be contained within it. But if you try to simply enchant an ordinary sword, it won't last. The sword must be crafted from the very beginning to contain the magical energies necessary for the effect you wish to create.