O.K., first Welcome to the board. Second, your set up will dictate how you transfer your wort.
The Reader's Digest version answers are:
1) When you transfer the wort to the fermenter, you want to aerate it to help the yeast get started. Pouring it and letting it splash a little will usually accomplish this. You will pitch enough yeast to overcome any airborne infection.
2) After fermentation, you don't want to introduce O2 to your wort/beer. It will cause oxidation and lead to off tastes. You do this by making sure your racking tubing goes to the bottom of your transfer vessels.
Now, if you're interested, I wrote up how I used to do it and why. When I was new, sometimes it was hard for me to understand some of the things in the books and I needed it broken down into plain English. Luck - Dwain
I recently started using a "no chill" method, but more on that later. I will tell you what I did and I'm sure someone will jump in and give you their method/explanation. This method worked very well for me for many years. My suppositions are that you are making an ale, using dry yeast and making 5 gal. batches. Also, I use an iodine solution to sanitize. Even though it's no rinse at the proper concentrations, I rinse it.
* Make sure your fermentor, lid, floating thermometer, measuring cup, small fork, air lock, and stopper are sanitized and rinsed if necessary.
* Pour you wort into your fermentor. At this stage, you want to introduce oxygen into the wort to help get the yeast started so splashing is a good thing.
*Cool your wort down to the desired pitching temp. You can do this with an ice/water bath around your fermentor. I did this in the kitchen sink. Put the stopper in the sink, put in a little water and put in the ice. Bring the temperature down to ~75F. Rehydrate your yeast while waiting on the temp to come down. Put about 1/2 cup of 70F - 90F water in your sanitized measuring cup, add your yeast packet and stir it with your sanitized fork. When the wort is at temp., take out your thermometer, take your wort out of the bath, dry it off and pour in your yeast slurry. Put the lid on it and put the fermentor wherever you are going to let it ferment. Remember, the closer you can keep it at 65F - 72F, the better off you are (although I couldn't maintain these temps during the summer until I got more equipment) and preferably dark. Once you are through moving the fermentor around, install your stopper and air lock. From this point forward, you want to minimize the oxygen introduced into the beer. It will cause your beer to oxidize and can produce off tastes. Back when I was starting, I would let it ferment for 2 weeks and rack it the bottling bucket. I didn't worry about the hydrometer reading back then. When you rack to the bottling bucket, sanitize your racking cane, tubing, tubing you will use to bottle and your bottle wand or equivalent, and measuring cup. Take the air lock out of the fermentor, and just put your fermentor on the counter, remove the lid and put something under one side of the fermentor so that it is at a slight angle (I use a piece of 2X4). Try not to shake the fermentor. Put your racking cane in your fermentor setting on top of the trub. Your tubing needs to reach almost to the bottom of your bottling bucket. Start your siphon and catch about 1 cup of wort in a saucepan. Heat it slightly and put 3/4 cup of dextrose in the pan. Mix it up well and pour it in the bottling bucket. Once you have the beer racked out of the fermentor and into the bottling bucket, put the bottling bucket on the counter and start bottling