I've never properly used Linux before, let alone an ssh console server. I have no idea what to do, really.
You may want to consider: A Windows VPS; managed servers instead of DIY; or whether you're in over your head and should stop before you lose money. If you're still here and you want to learn, I'm happy to help.
I've tried googling for an hour now, and I did some stuff like compiling bitcoind (at least I think I did, I have a /home/bitcoin/ folder now..) but I don't even know if it's working. How do I install bitcoind, or any program really?
Most software can be installed without compiling. The distribution you choose will come with a whole bunch of software already prebuilt. For Ubuntu and other Debian-type systems, do "apt-get update", then "apt-get install aptitude", then "aptitude search <partial name of thing you want>", then "aptitude install <name of thing you want>". All those commands should be run as root.
For bitcoind, you don't need to build it yourself. Just get a precompiled one like this (As a non-root user):
tar -xf bitcoin-0.5.2-linux.tar.gz
A tar file is like a zip file, except it also stores unix-type permissions and ownership. In this case it stored the fact that bitcoind is set executable. You can see the permissions with 'ls -l'. Permissions are the column on the left with -rwxr-xr-x which means read/write/executable for owner/group/everybody. Read 'man chmod' if you'd like to know more about how that works.
bitcoind will bitch that you need to set an rpcpassword. To edit the config file:
Or just right-click, Edit in WinSCP.
How do I move files to the server?http://winscp.net/
How do I start programs?
If they're in your path ("echo $PATH"), just type their name (like tar and wget above). If they're not in your path, type the path to them and then their name - for instance "./bitcoind" above which means to run bitcoind in the current directory.
Most services have startup scripts to do extra stuff when they're started. Take a look at "ls /etc/init.d" to see a list of those. For instance, "/etc/init.d/apache2 start" to start the Apache web server after installing it with "apt-get install apache2", or "/etc/init.d/apache2 stop" to shut it down.
How do I see what programs are running and how do I interact with them?
"top" to see a list similar to Task Manager
"ps axf" to see a tree of everything running
"ps axf | less" because it may be too long to fit on one screen
"killall bitcoind" to shut it down by asking nicely
"killall -KILL bitcoind" to force-shutdown
"kill <bitcoin's PID number>" (get the PID from the left column in the ps command) if you have multiple bitcoinds and you just want to kill one
"./bitcoind help" to get a list of RPC commands for bitcoind
"./bitcoind getinfo" as an example RPC command to bitcoind
Ask for anything else you need to do.