How is titanium metal obtained from natural resources?
Titanium is found as an ore, according to the Titanium Occurrences Wikipedia page, specifically, the 2 most economical ores are:

Ores of titanium

Rutile $\ce{TiO2}$ and Ilmenite $\ce{Fe^{2+}TiO3}$

Extraction of titanium metal from ore

According to the chemguide page Titanium, 


  Titanium can't be extracted by reducing the ore using carbon as a cheap reducing agent. The problem is that titanium forms a carbide, TiC, if it is heated with carbon, so you don't get the pure metal that you need. The presence of the carbide makes the metal very brittle.


Rather, the ore is chlorinated, then reduced as shown in the schematic from the webpage Titanium Exposed (the chemical processes are included):



Chemguide states that either $Mg$ or $Na$ can be used in the reduction stage, which adds to the cost of production as they need to be extracted themselves.

Asides from the links used in this answer, another good resource is Chemistry of Titanium (Professor John Lancashire - University of the West Indies)