In a House With a Basement 
Avoid windows. Get in the basement and under some sturdy protection (heavy table or workbench), or cover yourself with a mattress or sleeping bag. Know where hefty objects rest on the floor above (pianos, refrigerators, waterbeds, etc.) and do not go under them. They may fall through a weakened floor and crush you. 

In a House With No Basement  
Avoid windows. Go to the lowest floor, small center room (like a bathroom or closet), under a stairwell, or in an interior hallway with no windows. Crouch as low as possible to the floor, facing down; and cover your head with your hands. A bathtub may offer a shell of partial protection. Even in an interior room, you should surround yourself with some thick padding (mattress, blankets, etc.) to protect against falling debris if the roof and ceiling fail. 

In an Apartment, Dorm or Condo
If you live in an apartment on the upper floor, immediately get to the lowest level of the building that you can; this could be an underground parking garage or a neighbor's first-floor apartment. Then move to the most interior area possible, away from windows. 
If you live in a high-rise apartment building, you may not have enough time to get to a lower level, so picking a place in the hallway in the center of your building is the best idea, such as a stairwell.  If that is not available, then a closet, bathroom, or interior hall without windows is the safest spot in your apartment during a tornado.  Expect power loss during a tornado storm, so avoid elevators and keep a flashlight handy.

In an Office Building, Hospital or Store
Follow instructions from facility managers. Go directly to an enclosed, windowless area in the center of the building — away from glass and on the lowest floor possible. Then, crouch down and cover your head. Interior stairwells are usually good places to take shelter, and if not crowded, allow you to get to a lower level quickly. Stay off the elevators; you could be trapped in them if the power is lost. 

In a Mobile Home
Get out! Even if your home is tied down, you are probably safer outside, even if the only alternative is to seek shelter out in the open. Most tornadoes can destroy even tied-down mobile homes, and it is best not to play the low odds that yours will make it. If your community has a tornado shelter, go there fast. If there is a sturdy, permanent building within easy running distance, seek shelter there. Otherwise, lie flat on low ground away from your home, protecting your head. If possible, use open ground away from trees and cars, which can blow onto you. 

In a Car or Truck
Vehicles are hazardous in a tornado. If the tornado is visible, far away, and the traffic is light, you may be able to drive away from its path by moving at right angles to the tornado. Otherwise, park the car as quickly and safely as possible — out of the traffic lanes. Avoid seeking shelter under bridges, which can accelerate the wind while offering little protection against flying debris. 
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In The Open Outdoors
If possible, seek shelter in a sturdy building. If not, lie flat and facedown on low ground, protecting the back of your head with your arms. Get as far away from trees and cars as you can; they may blow onto you in a tornado.