The Sysinternals suite contains a lot of programs. Some of them have a GUI and some are command-line utilities (that is, you have to run them from a command line as opposed to clicking on them in explorer, just as mitchell65 said). Moreover, some of the programs included with the suite simply do not work in Windows 7.
Basically, you have to read the description on the sysinternals site - or the included README file. I will give you some examples.
The three probably most used programs in the suite are "autoruns.exe", "procexp.exe", and "tcpview.exe". These three have a GUI, so to run them, you just have to double-click on the files in explorer. Note, that sysinternals suite does not need to be "installed", you just unpack it to whatever folder you want and run from there.
As a counter-example, there is "rootkitrevealer.exe". This one does not run on Windows 7 x64 at all (not sure about the 32-bit version though, I don't have it).
An example of the command-line program is "whois.exe". Clicking on the file will result in brief flash of the command-line window only. This means you have to type "cmd" in the Start -> Search window, or go through your start menu, find All Programs -> Accessories -> Command Prompt.
Then, you have to navigate to the folder where your program is actually located. This means, if you simply start the command prompt and type whois.exe, you'll see nothing or rather the error message "whois.exe is not recognized ...". This is because the sysinternals suite is not installed and so the folder where it's located is not added to the "path" (i.e. the list of folders which the OS searches for executables when you type the name of an exe file in the command prompt). If you need to learn how to navigate to various folders within the command prompt window, ask for help, or read one of the tutorials here, or simply search in Google for the list of commands.
However, if everything is OK with your system and you have downloaded the most recent version of the suite, then when you run each individual program fro the first time it should exhibit a license window before everything else (where it tells you which utility you're running and asks you to agree to the licensing terms). If you run a command-line utility for the first time by clicking on the file what you will see is the licensing window and then the command line window. Of course, as soon as you agree to the licensing terms both will disappear - the program should be run from the command-line window.