The Finder itself is just an application. It is not a components library nor a framework. While you cannot "embed" Finder functionality in your application, you can influence Finder functionality and invoke Finder functionality.
First off, you can attach Folder Actions to folders. These will trigger when a user does something to the contents of a folder - for instance, they drop a file into it. You set this up in the Finder. You should to learn a little AppleScript, if interacting with the Finder is something you want to do.
Second, since the Finder supports AppleEvents, you can affect the Finder using AppleScript. Take a look at My First AppleScript and My First AppleScript Part II to see how to do this. Here is much more in-depth information, in AppleScript Overview: Scripting with AppleScript. Here is some More Finder Scripting.
Third, there is also support for developing ways for the Finder to do complex things for the user at the click of a button, using Automator (Mac OS X 10.5). You can also create a Service in Automator, beginning in Mac OS X 10.6 ("Snow Leopard"). Take a look at Automator and Finder Actions in Mac OS X 10.6 for an introduction to this latter technique.
Even though Finder windows themselves are not an embeddable component, if you really want to provide the ability to pen, Print, Delete, Duplicate, etc. Files/Folders, and navigate from Folder to Folder, you can develop a simple Folder browser in your application.
It should not be a huge amount of work to do this so long as you do not set your sites on mimicking the finder or duplicating all of its functionality, just the essential basics I have mentioned.
You would need to know how to program the Macintosh, however - not just use AppleScript. The normal way to do this would be to learn the Objective-C programming language and the Cocoa framework. You would need to get familiar with writing applications using a Model-View-Controller architecture.
You would create a subclass of NSObject named something like MyFile, and a subclass of a collection class named something like MyFolder. When the application creates the browsing Windows, and each time the application activates (becomes the frontmost application), you8 would refresh the contents of the browsing menu.
You could put a menu in your menu bar with commands in it: Open, Print, Delete, Duplicate. When the user does one of those commands, your application performs the appropriate actions itself or sends the request to the Finder. After the action has been completely carried out, then you refresh the browsing window for currently displayed Folder, or newly displayed Folder if the user navigated to a different Folder.
If you are familiar with design patterns, object-oriented programming, and frameworks in general - reading up on Cocoa Design Patterns will speed your learning curve immensely.
These are various techniques you can use to harness some of the power of the Finder. As you look these over, I suggest getting very clear in your mind just what benefit this brings to the user of your application. Writing down what the overall objective of this feature is, and what commands you wish to support, will make it easier to choose the path you take in developing it.
The user can always click on a Finder folder window at the click of a button, since Finder is always running. So avoid simply duplicating that functionality for its own sake. Focus on the benefit you are providing the user. Make sure that you do handle the situations where the user updates the Folder you are showing the contents of from another application and then switches back to your application.