First of all, you have to keep in mind that to work with the new features proposed by version 7.0 of the language, you will need to have Visual Studio 2017 (any version, including the Community Edition) or Visual Studio Code with the OmniSharp Extension (C# plugin), which also allows to use the language in other popular editors like Vim, Emacs, Sublime, Atom, Brackets, and so on.
Once you have that ready, C# 7 features will be available in the IDE and we can start playing with these additions. Also, it's important to note that Microsoft is encouraging the contributors of the coming versions of the language to deploy new features in a faster path, although including a smaller set of new features.
Actually, this version does not include something as foundational to the language as LINQ or async/await. C# 7 adds extra syntactic sugar in some cases, except its most powerful features: the new support for tuples and deconstructions.
Let's start with the "syntactic sugar."