This photo and component list might be helpful:
Here's the order I would choose:
First, I'm assuming that you didn't disassemble the fork/steerer (for a proper teardown, you would have at least partially removed the steerer to replace its bearings; that takes some experience and training, so don't worry about it for now).
I'm also assuming that you didn't remove the bottom bracket (the axle and bearings for the crankarms) or the crankarms, or the pedals. It's important that each of those be properly tightened to prevent damage or a fall, but we'll assume they're fine.
Details for the following steps are in the Park Tools website mentioned above, and also in the manuals for the various parts, which may or may not be available online.
From your photos, next you need to attach the rear derailleur to the derailleur hanger using the big bolt at the lower center of photo 9. First, make sure the derailleur hanger is not bent; it should be perfectly parallel to the plane of the rear wheel -- the more bent it is, the harder it will be to make the rear derailleur shift correctly.
Mount the rear wheel/cassette on the rear dropouts using the quick-release skewer. It'll be easier later if you already pump up the tire first and make sure it has no leaks.
Next, attach the front derailleur to the seat tube. You want the cage on this to be parallel to the plane of the front chainrings, and set a certain height above them when looking at it from the chain (drive) side.
Now, install a new chain. I strongly suggest one with a hand-openable "master link" such as the SRAM ones, for example the PC 830 here: http://www.amazon.com/SRAM-P-Link-Bi.../dp/B00161FWJG
You will likely have to shorten it using a chain tool. The instructions with the chain should show you how to size it correctly for your setup.
Now, you're ready to install and adjust the shifter cables. You'll need appropriate new shifter cables for your grip shifters. There's usually a hatch or similar opening in each shifter through which you can thread the free end of the new cable from the inside out through the barrel adjuster tube (the other end will have the anchor). From your photos, it looks like you might be missing the small threaded caps with holes through them that are the barrel adjuster caps -- be sure to install those on the barrel adjusters before installing the cables.