How can ISPs on one continent connect to ISPs on another continent? From a physical layer standpoint? Say one ISP is located in Asia and another one in Europe how would they connect their fiber optic cable to exchange traffic? Also how would they connect physically through IXP (Internet Exchange Points) http://en.wikipedia.org/wiki/List_of_Internet_exchange_points_by_size Do they have to drag their fiber optics cable all the way to these locations?
There are a number of things ISP's do:
The last option is most common. There is only a limited number of transit providers who don't buy transit from another ISP, they're usually called Tier 1. Most ISP's combine IXP connectivity and IP transit for their global connectivity.
Here's a real world example: I used NLNOG Ring's
As you can see from this example, a lot of networks reach Facebook via DE-CIX (the IXP in Frankfurt, Germany, one of the largest in the world), but there are also a large number of networks which use Telia (AS1299) and NTT (AS2914) to reach Facebook. Telia and NTT are tier 1 transit providers.
Edit 2: Since the image is downscaled it's hard to read. here is a fullsize version.