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How to download Packages for Android Studio?

I just started Android Development yesterday and just finished with my first Activity. On running it, I'm getting errors like
**Error:(4, 37) error: package android.support.design.widget does not exist**
As I never post without it, I've already done plenty of searching on this. Basically, what I've understood is that it couldn't find that Widget Package on my PC. So, do I have to download it? If yes, then how?
People on internet had similar problem with Packages and almost every post has different answer to this. Some say change your Gradle File others say Update your Studio (have done it).
Any kind of explanation or bit of knowledge with the solution would be highly appreciated. I'm a kind of geek who want to get concepts and basics clear. So, it would be great if you include the reason and technicality behind this too with your answer. Thanks. :)

It's a design library for Android apps development and as #Dominique pointed have a look at that page and copy paste that compile 'com.android.support:design:22.2.0' line in your project gradle file and press the sync button. Your project will sync in a few moments and the design library will be downloaded. Now you can use this library and there won't be any errors.

No, in Java "package" is not a "library" or a "piece of software" (like it is in some other languages). Package is what classes belong to - you might think of packages as directories containing Java files (it is a simplification, but it works). In Java libraries are packaged into (usually) "jars" (those jars usually contain classes divided into packages), so what you need to download is "jar".
So, first thing you need to check is: what library contains the package, and configure your IDE accordingly. The package in question belongs, I think to the so called android support library, which you can install using the SDK tool.

Import Neo4J API in Netbeans

For a project I am building a Java GUI from which queries can be sent to Neo4j, to make it easier to do particular analyses. To get this all working, I have downloaded a .jar folder containing all relevant classes (neo4j-javadocs-2.1.7-javadoc.jar). I have loaded the library through the project->properties->libraries->Add JAR, but I can't seem to import the classes I want to use in my GUI (neither automatically nor manually).
I am dabbling in Java, so it is probably a basic oversight that I am making, but with the help from tutorials online and trying different commands (like entering the path of the .jar file) I can't get it working. One of these tutorials is specific on the Neo4j library, so I am very confused. That tutorial is written for Eclipse, instead of NetBeans which I am working with, but as far as my knowledge goes that shouldn't matter for the commands
I don't have enough reputation to post direct images, but this link contains a screenshot. If more information is required, let me know. http://i.stack.imgur.com/lUytK.png
Additionally, when I normally add a class that is not imported, there is an automatic function to import the class. This option is missing for my specific class, so maybe I added the library in an incorrect way?
http://i.stack.imgur.com/QeDX4.png
Edit: Issue resolved thanks to a colleague that came in. Apparently I loaded the Javadoc where I should have loaded to individual classes from the lib directory.

It really should work.
Try to save all changes. NetBeans reparses the classes when you save them.
Try to build your project manually from command line using Ant build script

Use Maven, Ivy or Gradle for Dependency Management then you can depend on the Neo4j artifacts.
For sending queries to the server you actually don't need Neo4j artifacts.
You can also use the JDBC driver, see http://neo4j.com/developer/java

Creating a custom FileSystem implementation in Java

I read on oracle that it is possible to create a custom FileSystem, but I can't really find much documentation on creating one. Could anyone link me to somewhere I can learn more about custom FileSystems?
Where I read about this:
http://docs.oracle.com/javase/7/docs/technotes/guides/io/fsp/filesystemprovider.html

A (Real) Simple Example
A very simple Java FileSystem to use as an example is nodet/githubfs. There are only a few classes and it will give you the flavor of how to implement a basic file system. The primary classes are:
GitHubFileSystem
GitHubFileSystemProvider
GitHubPath
Note that this file system does not implement all operations (which is part of the reason it is good as a high level example).
Experiment!
To experiment with using a custom FileSystem without any coding, a handy project is puniverse/javafs. It allows you to mount it as a FUSE and interact with it from a terminal. Setup is quite easy:
import co.paralleluniverse.javafs.JavaFS;
...
// Need to mkdir /tmp/mnt first
JavaFS.mount(fileSystem, Paths.get("/tmp/mnt"));
Thread.sleep(Long.MAX_VALUE);

Google opensourced a completely in-memory filesystem implementation called JimFS: https://github.com/google/jimfs

I know this is an old question but many people still want the actual answer, which is not here. The problem is that the documentation by Oracle (Sun), listed by the OP is missing critical information. What adds to the confusion is that the "demo" referenced by the doc is packaged in a confusing way. There is a Demo.java source file and src.zip and a zipfs.jar. The Demo.java is NOT a FileSystemProvider. Its a custom FileSystem. For it to work you have to add the zipfs.jar to the "extensions" folder of your JRE/JDK, so that when the Demo.getZipFSProvider() method is called, it will find the custom FileSystemProvider which returns the custom FileSystem. If you look in the src.zip you will find the code for the provider. If the Java documentation had been properly written this question would not have come up. Its confusing. Even the readme file in the demo makes no mention of the provider. Sad.

Not able to find sun.awt.image.codec package

I searched a good lot but all in vain.
I want to get the source for sun.awt.image.codec.* java package.
Any help will be very appreciated..
Thanks
EDIT
Actually I have to use that package only, its required for my work. Its necessary for me since I am doing a performance eval [i can't change the code].

Update: This code is proprietary and the sources aren't available.
Try to use a decompiler or write black box performance tests.

Maybe you use OpenJDK? Install oracle jdk and try then.

Any website with a list of thirdparty java libraries?

I'm wondering if there is a website with like a list of java libraries/jars where you can browse around and see if theres something you could use. like when you make your own program which then contains lots of useful stuff.
Sort of like a website where people share their code, for public use.

SourceForge
Freecode (Freshmeat)
Google Code
github
Java.net

http://mvnrepository.com - if you know jar name or package name. it will provide you available versions and pom/ivy/gradle coordinates for copy/paste.
http://findjar.com/ - helps you to find jar containing this f*%^ing class nobody knows about (and then you can search mvnrepository to look if it is available for maven build - if not, the best is just ignore this library as this is probably of low quality or not yet released to public properly)