In order to open access to a tree, one has to adopt the main policy of that tree.
The amount of culture required to open up another policy increases with each step and scales with the number of cities, the more cities the more expensive it becomes to adopt another cultural policy.
More policy trees become available once an empire enters a new era.
During gamescom we copied down the Ancient and Classical Policies, which can be found in the first four policy trees. The first three are available from Ancient on, Piety can be accessed once reaching Classical.
Cultural Policies screen
I. Tradition: +1 food per turn in capital
2. Aristocracy: +33% wonder production
3. Monarchy: Buying tiles 50% cheaper
--> requires: Oligarchy
4. Landed Elite: 33% faster growth of capital
--> requires: Oligarchy, Aristocracy
5. Legalism: 33% less unhappiness from population in capital
II. Independance: +50% production of settlers
2. Republic: +1 production in each city
--> requires: Collective Rule
3. Citizenship: +25% production of workers
4. Representation: +1 culture in each city
--> requires: Citizenship
5. Meritocracy: +1 happiness for each city connected to the capital
--> requires: Citizenship
III. Honor: +25% combat against barbarians
2. Military Tradition: Units gain double experience from combat
--> requires: Warrior Code
3. Discipline: +15% combat for units that stand next to another unit
4. Military Caste: City Garrisons decrease empire unhappiness by 1 each
--> requires: Discipline
5. Professional Army: Upgrading units costs 50% less gold.
--> requires: Military
IV. Piety: +2 happiness
2. Theocracy: -20% unhappiness from population in non-captured cities
--> requires: Organized Religion
3. Reformation: Begins a 6-turn Golden Age.
--> requires: Organized Religion
4. Mandate of Heaven: 50% of excess happiness converted to Culture.
5. Free Religion: 2 Free Cultural Policies.
--> requires: Reformation; Mandate from Heaven
(I like that...if that's the case.)
You can and should plan ahead which path you want to go.
It´s also gonna depend a lot on the culture your empire is accumulating how many policies you´ll be able to adopt. Constructing buildings providing culture obviously allows for more policies, but at the cost of other stuff (like units) you might have built. Same is true for getting a Great Artist to push culture over another GP etc.