Make sure your library got added successfully.
Check the following things.
1.Your build.gradle should be like
dependencies {
compile 'com.android.support:support-v4:19.0.+'
}
2.File > Project Structure > Modules >Dependency Tab There should not be any red mark in dialog showing error if they are fix them.
3.Check your Module_Name.iml file
It should have this entry in last section
<orderEntry type="library" exported="" name="support-v4-19.0.0" level="project"/>
If its there with no entry close you studio delete .iml file and open studio again wait for gradle sync to be complete.You .iml file will be created again check for entry.
If every thing is fine do sync Your project with gradle again using this lovely tiny gradle button in toolbar.