A racking cane is basically just a long piece of tube with a curve on top. You attach a length of tubing to it and it allows you to siphon liquid from one container to another. You could probably just use plain flexible tubing for this, but a metal one is nicer since it allows you to put the intake point exactly where you want it (e.g., away from the trub).
After you've made your wort, it's maybe 200 degrees or so. You want to get it down to about 75 degrees or so as quickly as possible because this is a prime time for infections to occur in your beer. The faster you can pitch your yeast, the better. So folks use an immersion chiller (there are other fancier types, but the immersion chiller is a piece of cake). Buy about 20 feet of 3/8" copper tubing. Wrap it in a coil that will fit into your brew kettle with BOTH ends sticking up out of the pot. Attach two lengths of tubing to run from your faucet or water source to the chiller, and back. Once the wort is ready, you attach one end of the chiller to your faucet and the other into the drain and turn on the cold water. The cold water runs through the copper tubing and by the time it exits the other side, it's up to about 180 degrees or so. Just keep running the water through until you've reached the proper temperature for the yeast.
Instead though, a lot of guys just carry the brew kettle to their bathtub and immerse the kettle in cold water. That works too. You can also use ice inside of sanitized ziplock bags for this. Basically, sanitize 2 ziplock bags, fill one with water, close it, put it inside the other bag, and freeze it. Once your wort is done boiling, you remove the inner bag from the outter bag and throw the sanitized inner bag with the ice
sealed inside it into the wort. Once the ice has melted, remove the bag with the water still inside. You might also be able to sterilize some plastic freezer packs and use those too. Basically, anything to get the temperature down as quickly as possible. I think the immersion chiller is the most fool-proof of the methods. No risk of spilling/dropping/splashing on the floor, no risk of water leaking out of the bag, etc.
An airlock is simply a device designed to let CO2 out of your fermenter without letting air inside. It sort of forces the CO2 to travel up, down, and back up. You have a straw that sticks up, maybe, 3 inches. Then you have a "hat" that sits on top of it and drops down 3 inches. And that all sits inside a container with a lid that has a couple holes in the top. You fill the container half way with water (or alcohol). When the CO2 leaves the fermenter, it goes up the 3" tube, and enters the "hat". The hat tries to float upward out of the water/alcohol, but it is held in place by the top of the container. So then the CO2 builds up until it forces its way past the alcohol in the bottom of the container, and then up and out the top. It's harder to explain that it really is. Do a Google search and look at a few pictures and it will be quite obvious how it works. Again, they're about 4 inches long total and you can buy them for a dollar from a homebrew shop here in the states. You can also just use a blow off tube (3/4" or greater inside diameter), run it out the top of your fermenter and down into a bowl/jug/pail of water or alcohol. It's not quite as sanitary, it takes a little more space, and it doesn't allow you to observe the fermentation process quite as easily, but technically it will work just as well... if you go this route, just be sure you have a hydrometer so you can check your fermentation that way.
The aquarium pump is used after transferring the wort into the primary fermenter, but before you pitch your yeast. You will want to aerate your wort so that the yeasties can multiply to ensure a vigorous fermentation process. The trick here is to try and be careful to prevent contaminants from sneaking into the air supply. For this, people will use sterile cotton cloth, perhaps dipped in alcohol, between the pump and the wort. Again, there are easier and less effective methods. You can simply shake your wort and splash it around a bit. That works too and it's free. If you use the pump, they say to run it for a half hour or so.
OK. I'm tired of typing now. You've worn me out. There are PLENTY of good basic brweing resources on the internet. Go find a couple and read them before you ask any more questions.