It is not possible to change the game pace once the game has already begun. 

[This article][1] details the mathematics behind these mechanics and details how they're effected in the various game speeds. 

[This thread][2] from the Steam forums details the effects the game speed has in less mathematical terms and also includes information on how map sizes effects gameplay as well.

Game speed effects a fairly substantial number of the mechanics in the game, including but not limited to;

- The amount of production required to complete units/structures
- The amount of science required to learn new technologies
- The amount of culture required to purchase new policies
- Gold from defeated barbarian tribes
- The cost of research agreements

For example; *(copied from the [Steam link][2])*

**Game speed: QUICK**

- Game Length (Turns) = 330, 
- Production Cost (Hammers) = 26, 
- Policy Cost (Culture) = 15

**Game speed: STANDARD**

- Game Length (Turns) = 500, 
- Production Cost (Hammers) = 40, 
- Policy Cost (Culture) = 25

**Game speed: EPIC**

- Game Length (Turns) = 750, 
- Production Cost (Hammers) = 60, 
- Policy Cost (Culture) = 35

**Game speed: MARATHON**

- Game Length (Turns) = 1500, 
- Production Cost (Hammers) = 120, 
- Policy Cost (Culture) = 75

<sup>*Product cost = Cost (In Hammers) to produce a WARRIOR.*<br />
*Policy cost = Cost (In Culture) to produce the 1st policy.*</sup>

In addition, the game speed also [affects the number of turns in each game][3].

  [1]: http://civilization.wikia.com/wiki/Mathematics_of_Civilization_V
  [2]: http://forums.steampowered.com/forums/showthread.php?t=1580535
  [3]: http://gaming.stackexchange.com/q/9186/27134