To get started with Racket, download it from the web page and install it. If you are a beginner or would like to use a graphical environment to run programs, run the DrRacket executable. Otherwise, the racket executable will run a command-line Read-Eval-Print-Loop (REPL).
On Windows, you can start DrRacket from the Racket entry in the Start menu. In Windows Vista or newer, you can just type DrRacket. You can also run it from its folder, which you can find in Program Files → Racket → DrRacket.
On Mac OS X, double click on the DrRacket icon. It is probably in a Racket folder that you dragged into your Applications folder. If you want to use command-line tools, instead, Racket executables are in the "bin" directory of the Racket folder (and if you want to set your PATH environment variable, you’ll need to do that manually).
On Unix (including Linux), the drracket executable can be run directly from the command-line if it is in your path, which is probably the case if you chose a Unix-style distribution when installing. Otherwise, navigate to the directory where the Racket distribution is installed, and the drracket executable will be in the "bin" subdirectory.
If you are new to programming or if you have the patience to work through a textbook:
How to Design Programs is the best place to start. Whenever the book says “Scheme,” you can read it as “Racket.”
Continue: Web Applications in Racket introduces you to modules and building web applications.
The Racket Guide describes the rest of the Racket language, which is much bigger than the learning-oriented languages of the textbook. Since you learned functional programming from the textbook, you’ll be able to skim chapters 1 and 2 of the Guide.
If you’re already a programmer and you’re in more of a hurry:
Quick: An Introduction to Racket with Pictures gives you a taste of Racket.
More: Systems Programming with Racket dives much deeper and much faster. If it’s too much, just skip to the Guide.
The Racket Guide starts with a tutorial on Racket basics, and then it describes the rest of the Racket language.
Of course, you should feel free to mix and match the above two tracks, since there is information in each that is not in the other.