You can use Apache Common libraries: http://commons.apache.org/ and it's utility classes :-)
Here's how to do it:
1. Go to: http://commons.apache.org/proper/commons-io/download_io.cgi
2. Download the library: commons-io-2.5-bin.zip (SEE THE IMAGE BELOW)

3. UNZip it
4. Use ONLY THE FILE commons-io-2.5.jar
5. Copy the library commons-io-2.5.jar and put it into your project by creating new directory named lib and pasting it there
6. Add the library to the project by clicking on it with the right button and choose Add as Library (now everything in this .jar file is available to your project)
7. See my code
The Code:
import org.apache.commons.io.FileUtils;
import java.io.File;
import java.io.IOException;
public class CopyFilesMethod3ApacheCommons {
public static void main(String[] args) {
File sourceFile = new File("files/loremipsum.txt");
File targetFile = new File("files/target.txt");
try {
FileUtils.copyFile(sourceFile, targetFile);
System.out.println("File is copied!");
} catch (IOException e) {
e.printStackTrace();
}
}
}
BTW you can use it with your Android projects.