Identifying magic items is more of an art than a science, and the primary tools of the art are Detect Magic and Identify.
Detect Magic
By casting Detect Magic, your eyes gain the ability to see in the spectrum of magical light. Magic appears to you as beams of light, colored and shaped by the nature of the magic you see.
While using this spell, you get Advantage on any Arcana checks made to identify magic within range, and if successful you learn the basic function of the target item or spell.
Identify
When you cast Identify, you magically command the item to reveal its instruction manual. This appears as a magical script that hovers over the item.
Each magical item has two sets of instructions: the creator's instructions, and the metaphysical footprints.
Creator's Instructions are left by the item's creator upon completion of the item. For the most part, these instructions are pulled from the creator's subconscious by the creation process. However, skilled craftspeople can choose to leave (or omit) any instructions they desire as part of the creation. These instructions can be easily accessed by a 1st level Identify and are written in the creator's primary language.
Metaphysical Footprints are descriptions of the item's metaphysical footprint on the universe. They are formed by the very act of creating the item and usually manifest as arcane equations. You can learn anything you want about the item by studying its MP as long as you can figure out what they mean.
Reading the Creator's Instructions
Accessing the Creator's Instructions for a given item is as simple as casting Identify. These instructions are entirely up to the item's creator, but usually contain general instructions.
Interpreting the Metaphysical Footprints
Accessing the Metaphysical Footprints for a given item first requires that you cast Identify using a spell slot at least as high as the item's Tier. Each spell level beyond the item's Tier grants a +2 to interpretation checks.
Once the footprints have been revealed, you must attempt an Intelligence (Arcana) [Item Identification] Check for the type of information you are trying to interpret (listed below). On success, you learn that information.
Regardless of whether you succeed or not, this check requires you to Concentrate for 1 hour per Tier of the item in order to perform arcane calculations and research.
If you fail, you can reattempt the Check after completing a Short Rest. On the next attempt, it takes half as long and you have Advantage.
Interpretation Check DCs
Identify item's tier: automatic with first casting of Identify
Identify relevant schools of magic: automatic with first casting of Identify
Identify the primary functions: 10 + Double Item's Tier
Identify how to activate one function: 13 + Double Item's Tier
Identify a secondary function: 10 + Item's Tier
Identify side effects: 10 + Item's Tier
Is it cursed? 13 + Double Item's Tier
Identify a curse: 15 + Double Item's Tier
Who made it? 15 + Item's Tier
How long ago was it made? 15 + Item's Tier
Where was it made? 15 + Item's Tier
Identify primary spell used to enchant: 15 + Item's Tier
Identify primary magical component: 15 + Item's Tier
What is its purpose? 15 + Item's Tier