depends on the program and shell and OS and user agreements
Best bet isn't just to install programs. You can't install programs in the normal way, since your not ROOT. There are ways around it, but it takes some decent knowledge of compiling programs and stuff like that.
First off you only have access to your home directory and maybe a couple others. You have to figure out how to get the program to work in just your home.
If you find a binary (pre-compiled) program that may work. If it's Linux look for slackware packages. They can be untarred and the program taken out of them and then manually placed in a custom ~/bin directory. (~/ = home). It's a crapshoot if randomly downloaded binaries will work or not, unless you know what your doing.
If it's something other then Linux, I don't know.
To download files you can use text browsers, Lynx and Links are common. You can use wget command to get files off of the internet. Especially usefull with cut-and-paste technics.
wget
http://my.unix.warez.com/hell/uberhacks/shellhack.tgz
you can use the ftp command for ftp sites:
ftp my.unix.ftp.warez.com
AFter you download the stuff, you have to make sure that ~/bin or whatever your installed it in is in your path.
IN a BASH shell
echo $PATH (to check and if not there

export PATH=$PATH:~/bin
Your best bet is to ask politely for a administrator to install a program for you. Unless your allow to install your own programs and stuff you'll probably just piss them off otherwise.
They probably have lots and lots of programs there already that you just have to learn howto use. Most shells have community games, forums and stuff like that for asking questions and getting help.
For accessing a shell from a Windows Box I recommend putty.exe It can do ssh for a secure shell, but supports telnet and other telnet-like protocols.