preserve / conserve

When you conserve something, you ensure that you make use of it wisely. You make sure it is not wasted. There is a suggestion that if you do not make careful use of it, then chances are it will be impossible to replace the commodity. 

During the summer, the government always tells us to conserve power and water. It's okay to waste them during the winter months, but not during the summer. When you conserve something, you do not wish to waste or deplete any of the available resources. You attempt not to change anything drastically. 

• The Minister asked the people in cities to conserve water. 
• The fast bowler conserved his energy by shortening his run-up. 
• During the summer, theater owners conserve energy by switching off the AC.

Preserve, on the other hand, suggests that you make attempts to keep something as it is, without making any changes. In other words, when you preserve something you keep it intact. You keep it safe, protecting it from danger. 

• Our government doesn't do a good job of preserving our monuments. 
• We must make an effort to preserve our forests. 
• This is a beautiful old house. We must preserve it.