To learn a discipline that is not part of your clan, you need two things. A teacher, and some blood from a kindred that has that discipline as their clan discipline. The difficulty of learning said disciplines, however, changes.

Disciplines are divided into three groups. Common, Uncommon, and Clan Disciplines.

Common Disciplines
The common disciplines are:

Fortitude
Potence
Celerity

All Kindred can learn these disciplines with little issue. It just takes time and practice. The ST will tell you how much at each dot level. For dots 4+ you will need blood from a kindred who has this discipline as a clan discipline. Dots 1 - 3 can be learned with just time and effort.

Uncommon Disciplines
The Uncommon Disciplines are:

Presence
Obfuscate
Animalism
Auspex
Dominate

To learn these disciplines, even at the 1 dot level, you need both a mentor willing to teach, and blood from a kindred who has the desired discipline as a clan discipline. One dose from a clan will allow you to learn dots 1 to 3. But to learn 4+ you need a second dose of blood, from a kindred of a different clan that calls the discipline a clan discipline. For example. A dose of gangrel blood would allow a kindred to learn dots 1-3 of animalism. But to learn dots 4-5 they would need a dose from a Nosferatu. Dots 6+ might require yet another dose, from a tzimisce, for example.

Clan Disciplines
The final group of disciplines are Clan Disciplines. Those disciplines that are limited to a single clan. All bloodline disciplines count as clan disciplines in this regard. The Clan Disciplines are:

Obtenebration
Protean
Serpentis
Quietus
Chemistry
Dementation
Thaumaturgy
Necromancy
Vicissitude
Any discipline unique to a bloodline

Learning Clan Disciplines is nearly impossible. But if you can find someone willing to teach you, it is possible to learn. The same rules as learning Uncommon Disciplines apply, though in some cases, specifically with some of the bloodlines, it is impossible to learn more than a dot or two in their bloodline discipline, if possible at all.

Most clans jealously protect clan locked disciplines and will actively hunt down any kindred that dares delve into the secrets of their blood, as well as the mentor who was foolish enough to teach. YOU HAVE BEEN WARNED.

The Thinblooded
The Thinbloods hold a special power among the kindred. If a Thinblood knows a discipline, his or her blood is a viable source for others to learn that discipline… and Thinbloods treat ALL disciplines as 'uncommon' for the purpose of what is required to learn them. Though the same restrictions apply as well. Such as being hunted for learning Thaumaturgy.

Trial Through Combat
If a kindred attacks and drinks the blood of an enemy in battle, this counts as receiving a dose of their blood, but it does not satisfy the mentor requirement of learning a discipline.

Where Diablery comes in
If you Diablerize a vampire, you gain all of their discipline knowledge, and all of their blood. This allows you to satisfy both the blood and mentor requirements for both common and uncommon disciplines for up to dot 3. It does NOT however, satisfy the mentor requirement for Clan Disciplines or dots 4 or 5 of a common or uncommon discipline.

Elder Disciplines and you
Even if your generation allows you to learn them, your character will not be able to learn 6-dot or higher disciplines. They are called Elder disciplines for a reason and can easily break the game. Needless to say that those levels are very difficult to obtain and will always require a teacher. And there are no Elders in Jacksonville willing to give away those secrets just to anybody.