How can I prevent mineral build-up from my water?
Sounds like classic symptoms of hard water. Others:


Spotty dishes, clothes that don't seem to get clean without using a lot of detergent.  
Soap doesn't get very "sudsy" when you get it wet.
Soap scum on your bathtub.
Buildup of mineral-like crust on shower-heads.
Water softener heating element failure.  


You are very likely going to need a water softener to solve the problem.  

Diagnosing: 
Most hardware stores sell kits to test your water hardness that are very easy to DIY. Some stores that sell water softeners even have free test strips next to the water softener display. 

Also, if you are not put off by a big sales pitch. Companies like Culligan will generally do a free water evaluation for you so they have an in to sell you their products/services.