Ascending from one Tier of Spells to another is different depending on the Tier.
Note that regardless of Tier, it is impossible to learn magic off another PC.
Please note that you may not learn more than one spell per turn. You can, however, spend AP towards beginning learning a new one after you've attained a spell.
To learn basic Magic a Would-Be Mage must consult both a tome of magic and be taught the simple secrets of their art by an Adept.
To learn Tier One Magic, you must spend 2 AP to search for a willing teacher. After this, you will learn a single Tier One spell. Researching for a willing adept is a good start rather than just stabbing-in-the-dark to find one. Influence can be a good tool for demanding mages pay you attention.
If you already know one Tier One spell, you must search for another adept willing to teach you the other spell.
It is impossible to learn a magic if you already know a different magic. The Arts are fickle and don't like sharing space with each other inside a single mind…
To learn Expert Magic, an Adept must search out a hidden library of magic. Many such exist in the countries of the magic's birth, although all are heavily guarded, swept in mystery and hidden remarkably well, either underground, within universities, within Places of Worship, or buried deep under the desert as a means of protection.
To learn Tier Two Magic, you must spend (minimum) 2 AP to study at a Hidden Library. Knowledge of the whereabouts of these bastions of arcane knowledge are well hidden, and will need to be Researched before accessed. Once accessed, simple proof may be needed to attend the library and get past it's guardians. After this, you will learn a Tier Two spell.
To learn Tier Two Magic, you must know two / both Tier One Spells. You will be denied access otherwise.
If you already know one Tier Two spell, you must search for another library to teach you the other spell. It may be possible to return to the same library, depending on the Guards.
To Master Magic, you must seek out another Master of the Arcane. Masters are those that have truly exceeded the limitations of human consciousness, and have garnered absolute control of their sphere of the Arcane. Seeking out one may be hard, as the Masters ahve used all their power to either make them self scarce or protect their interests. It may be equally hard tracking down an elusive Hedge Master Fakir as it is convincing an all-powerful and arrogant Hermetic Archmage to teach you.
To learn Tier Three Magic, you must spend (minimum) 2 AP to study at the feet of a Master Magician. This will be nail-bitingly-hard to accomplish without solid Research, nerves of steel, and a willingness to learn. To this effect, Master's may require more than mere cajoling to teach a student, thus often more XP must be spent to chase the elusive Master, retrieve an artifact of his choosing, or contend with him in magical combat. After this, you will learn a Tier Three Spell.
To learn Tier Three Magic, you must know two / both Tier Two Spells. You will be denied study otherwise.
If you already know one Tier Three spell, you must search for another Master to teach you the other spell. It may be possible to return to the same Master, depending on the attitude, but they ask to prove yourself again.