The most important part of learning Linux is using it. The items the others have suggested are all valid, but a little general.
If you want to be a sysadmin, it's probably a good idea to learn your way around
CentOS, with is a free spin of Red Hat Enterprise Linux (RHEL). RHEL and CentOS are heavily used in the Enterprise. You could do this by installing it in VirtualBox or other virtualization software, if your computer has enough resources, which is also a good thing to get familiar with, since many enterprises use virtual machines. If you don't have a Linux computer, you can install any Linux distro in VirtualBox on Windows and even integrate it into your home network (that's another post).
As for further learning, learning is easier when it's fun. I would suggest that you pick out something you want to do, such as
* set up a home network.
* record a podcast.
* create a website.
* manage a blog.
or something else that strikes your interest, and do it with Linux. In the process of learning how to do that thing, you will learn more about Linux. Then move on to something else you want to do and learn more things.
Use the command line as much as possible, because, in the enterprise, many servers run "headless," that is, without a monitor, and are administered remotely via the command line, but don't be afraid to use GUI tools if you get stuck--get the job done, then go back and investigate the command line. They are administered via ssh and the command line.
That will give you a good foundation in the basics, so you can then move on to learning the stuff you have to learn.
I recommend this book as a great introduction:
http://tille.garrels.be/training/tldp/. Machtelt Garrels's Intro to Linux.
