Install Ubuntu (Debian based) - it makes life so much easier when you're starting out with UNIX based systems, partly due to the power that aptitude (it's pacakage management system) provides, but also because of it's excellent driver support! Fedora's (RedHat based) yum and Gentoo's emerge are close runners-up in this regard (but Gentoo is something to aim at installing when you have been using Linux for a good while - or, if you want to throw yourself in at the deep end).
Incidentally, Gentoo is my personal favourite and really hones your skills. It also compiles everything from source, so really allows you to optimise your system through compile flags etc. It has an excellent handbook you can follow to install, but is no easy task. If in doubt, go with Ubuntu - or BioLinux is cool too (similar Fedora one here too), as it has a lot of the software and libraries you may need for bioinformatics pre-installed. It is based on Ubuntu 10.04, so is a little outdated, although 10.04 is a long-term support release.
There is a lot to be said for trial and error. If you have an old machine you don't mind messing around with and testing out commands on, then install it on that, or if you don't then install it in a virtual machine using the likes of VirtualBox and you don't have to worry about breaking anything and can hack away to your heart's content. One useful thing with Virtualbox is you can find images already setup to run straight away - e.g. http://qiime.org/install/virtual_box.html.
Join this Google user group http://groups.google.com/group/unix-and-perl-for-biologists?pli=1, check out http://www.omgubuntu.co.uk/ and feel free to ask questions here http://askubuntu.com/.
Check out http://www.linuxjournal.com/, http://www.linuxformat.com/, http://www.linux-mag.com/ and http://www.linuxpromagazine.com/.
Read the UNIX and Perl Primer http://korflab.ucdavis.edu/Unix_and_Perl/ and the new book coming soon http://www.amazon.com/Unix-Perl-Rescue-Keith-Bradnam/dp/1107000688, which also has a site http://unixandperl.com/.
Documentation is rife for most UNIX and Linux tools and you can either use man, or simply Google most things and come across a plethora of answers (e.g. Linux man pages). Also, browse Linux.com, look at their tutorials, documentation and this link.
Any of the O'Reilly books are great.
IRC seems to be used less these days, but is an excellent resource - I hang out in #freeside and #hulllug at irc.freeside.co.uk (run by CS department at Hull University), but there should be UNIX/Linux channels on most IRC servers - e.g. http://justlinux.com/forum/showthread.php?t=107414 - freenode is arguably the best?