If you're running on Windows it is good to run Jenkins as a service so it starts up automatically without requiring a user to log in. The easiest way is to run the Windows installer, linked from Jenkins' homepage. This also has the advantage of being easier to automate.
The manual way is to follow Installing Jenkins as a Windows service.Alternatively, you can install a servlet container like GlassFish and Tomcat, which can run as a service by itself, and then deploy Jenkins to it.
Since Jenkins was written to work on unix-like platforms, some parts assume the presence of unix-utilities. It is advised to install these as well on Windows. Install UnxUtils (this includes a shell that seems to work with forward and backwards slashes and does globbing correctly)(UnxUtils does not download), put it in the Windows PATH , and copy sh.exe to C:\bin\sh.exe (or whichever drive you use) to make shebang lines work. This should get you going. If UnxUtils gives you trouble (Fork Failed Errors), try Win-Bash.