From this page, download the "Core" binary distribution. Whether you download the .zip file or the .gz file (or the Windows installer if you're using that OS) is up to you - they're the same thing. The installation instructions are here.
The admnin application is no longer supported with Tomcat6. Initially it was expected to be there but was never released. Even now there is no news on any forums or blogs or else if it will be released. Alternative options include: - JMX - lambdaprobe