I Need to Shrink My Database - I just freed a lot of space
Some Initial Caveats:


It is generally known as a worst practice to ever shrink a production database or data file (Log files are another issue as this question talks about). I advise people to not shrink their databases in blog posts like this where I talk about "right-sizing" and good planning. I'm not alone there (Paul Randal, Brent Ozar, just to provide a couple more links). Shrinking a data file or database fragments indexes, is slow and laborious on your resources, can be a drain on your system and is just a bad thing to do, generally 
In this case, we all know the risk is there, we are prepared to deal with it, but we freed a lot of space that we know we'll never ever need again. So in this specific type of case - shrinking makes a lot of sense as one of our options.


If you've read about the concerns and risks and you still need to do this shrink because you freed a significant amount of space, hopefully the rest of this answer will help you out. But do consider the risks.

There are two main approaches two consider here:

1.) Shrink Yes, do the actual shrink - Consider using DBCC SHRINKFILE instead of DBCC SHRINKDATABASE, you have more control over what gets shrunk and how. This will cause some performance degradation for sure - it is a large operation doing a lot of IO. You can potentially get away with repeated shrinks to a target size that gets progressively smaller. 

This is the "A.)" example in the above DBCC SHRINKFILE link.. A datafile is being shrunk to 7MB target size in this example. This format is a good way to shrink repeatedly as your downtime window allows. I would do this in testing on development to see how the performance looks and how low/high you can go of an increment and to determine the expected timing in production. This is an online operation - you can run it with users in the system accessing the database being shrunk, but there will be performance degradation, almost guaranteed. So monitor and watch and see what you are doing to the server, pick a downtime window or period of lighter activity, ideally.

USE YourDatabase;
GO
DBCC SHRINKFILE (DataFile1, 7);
GO


Always Remember: - every time you shrink you fragment your indexes and should do an index rebuild if you are going to shrink in chunks over a prolonged period of time. You are now incurring that cost each time if you can't get it done all in one window.

2.) New Database - You could create a new database and migrate data to it. You would have to script the empty database out and all of it's keys, indexes, objects, procs, functions, etc. and then migrate data to it. You could write scripts for this or you could use a tool like SQL Data Compare from Red Gate or other vendors with similar tools. This is more setup work on your side, more development and testing, and depending on your environment may also blow out your downtime window also but an option to consider.

When I am forced to shrink a Database
If this were my environment, I'd look to leave a fair/hefty amount of white space in the data file because I like being a disk hog and like to be prepared for future/unexpected growth. So I would be okay giving space back if we just deleted a majority of the space, but I'd never trust those saying "but it will never grow again" and still leave some white space. The route I'd probably go with (sigh) is the shrink approach if I had smaller downtime windows and didn't want to incur the complexity of creating an empty DB and migrating data to it. So I would shrink it a bunch of times incrementally (based on how many times I thought I needed to based on my testing in dev and the desired size. progressively choosing a smaller file size)and then rebuild the indexes.. And then I'd never tell any one that I shrank my database ;-)