Bicycle Mechanics - What am I doing wrong?

Greetings,
I learned to ride a bike late (when I was 30) so I'm clueless when it comes to bike maintenance. However, with youtube videos and helpful bike maintenance pages I've learned how to replace the tire/inner tube and some spokes. It's quite fun however I cannot figure out how to properly install the rear derailleur. I just bought this bike today (beater bike for $20) but the derailleur which was an old version did not stick and came out in the car. So I bought one recommended from the shop (Shimano RD-TX75) but those instructions are difficult to understand. By the way, I apologize in advance if this subject has been to death, but I cannot figure out what I'm doing wrong. I've checked all kinds of videos on how to install rear derailleurs, but they're all different than mine and it seems as if each derailleur has its own way of going on the bike. I've posted a pic below. By the way the bike is a Schwinn Sidewinder.
Thanks
(i'm sorry the photo is upside down, i can't figure out how to undo that)

you need to remove the bottom pulley ,put the chain thou the cage like a backward " S " . meaning the chain go around the gear ( the 5 or more gears on the back wheel ) , put the chain on front of the derailer's top gear (pulley ) and then behind the lower gear (pulley) and put the bolt back into it . (the lower pulley ). here check this out http://www.parktool.com/blog/repair-help/chain-installation-derailleur-bikes , look near the bottom of the page to see what I mean .

observe chain path copy that. you can remove pulleys and reroute or remove & reinstall chain.269566

Your chain is going through the pulleys in the wrong order. All RDs are pretty much the same in basic design, yours should be much like the others you looked at.

You could remove and reinstall (correctly) the pulley as suggested above or you could make things easier for yourself now and the next time by obtaining a "master link" for your chain which can be opened and reclosed without tools. You will need to buy or borrow a chain tool for one-time use to open the chain and install the master link. Thereafter to remove the chain for cleaning or derailleur work you can just pop it open. I use master links on all of the chains that I install.

yes masterlinks sounds good. I already bought that tool today and while I might not use it for a while it's pretty handy today. I would have had the work done at the shop but i wouldn't get the bike back until thursday.

Anyways, thanks for the pictures/advice they're very helpful. I think I can figure it out now.

Cheers!

You might find this useful in threading the chain on your rear derailer;

http://www.madegood.org/bikes/library/thread-a-chain-onto-a-rear-derailer/

There's more on there to help you set it up too. Nerull is right, most rear derailers are pretty similar in design

If you're ever in doubt about how to thread a chain through a rear derailleurs (in front of the top pulley, behind the lower) look at the cage. They're all made to form guides along the chain path.