@wstbrewing did a fine job of explaining it for you, but I will add some thoughts of my own. The LOT thread started beer trading for many of us, myself included. I've now shipped and received, combined, probably forty or fifty (?) boxes of beer.
@Bender_Braus_Brewing Some supplemental information for you...
In the LOT thread you say what you want and the person granting you provides beers of those styles.
For the Fellowship (FotD) trades, it is quite different. There is one going on now, so you could theoretically get in on that should you grant WST quickly enough and ship quickly enough.
1) 48oz is the minimum to ship? As WST noted, it is the minimum. Sometimes people ship 48oz and other times people ship 84oz. A reasonable guideline to follow is to see what the person who you are granting shipped and try to reciprocate. It's not a contest (unless you win), but we all want to be fair with each other.
2) Whats best to ship - FedEx, UPS, USPS, etc? One of those three. USPS is fastest, but it can sometimes cost a few bucks more. You can also opt to ship in flat rate boxes and ship multiple boxes. UPS and Fedex are often cheaper but at the expense of more days in transit. NOTE: INSURE your packages. If they confiscate the package they will still pay out the insurance claim. I am speaking from experience, now with all three carriers. I have a reputation on here for getting caught...not a good reputation to have.
3) What is generally the cost to ship 48oz? Box size/dimensions, weight, and location factor into cost. Use 20lbs as your weight and go from there; that's a pretty good estimate.
4) Is there an ABV limit (minimum or maximum)? Do people typically request what styles (ie. stout/sour/IPA)? As long as it is alcoholic, we are okay. Styles are requested by the person who you are granting. If you do not have options where you are at for their preference it is okay to put yourself next in line after they are granted.
5) Does brewery size matter? (ie. Microbrewery vs. Nanobrewery vs. Large/Regional Brewery)? The idea is that you are shipping beer (etc) to someone who cannot otherwise get that beer because of a lack of distribution. The thread itself is named Local Only Trade because the idea is that you will ship beer that is only local to you. For example, there is a brewery about twenty minutes away that nearly stopped bottle distribution. In fact, I have been to four places that usually carry there beer, and there is nothing. That's what I would ship to someone. There is a website that you can use to see where the breweries near you distribute to; however, I forget the site name. I imagine someone will read this and know what I am referring to.
ADDED INFO
Some people also include glassware in their shipments. It's cool to get glassware from other breweries, shirts and other stuff is also accepted (size matters). I am a little odd in that I'll send Mexican grocery items across the country, too, such as chorizo, mangoes, jack fruit, Mexican candies, ... you name it.
You will also see that people will include their homebrew in grants; however, those should never been counted towards the ounces. They are usually doing it because we enjoy feedback from each other. It's a brewing forum first and foremost...the trades only add to it.
There is plenty of information on the internet on how to package beer. Some things to remember: line the entire box with a trash bag, and inside the trash bag is the beer. The idea being if something breaks, the bag conceals it. Each beer should be wrapped in bubble wrap and someone sealed in it's own bag. Some of us use food sealers. They're great at protecting spills should something break.
I will correct WST on this one aspect. If you ship something to someone, and for any reason it does not make it there you are obligated to replace that shipment. Now, if you ship 10 beers to someone and one of those breaks you are not obligated to ship anything else. In cases where glassware was sent and arrived broken, or a really unique beer that you wanted the person to taste arrives broken, the person who shipped it will oftentimes replace whatever got damaged. In the cases of glassware, use the insurance. If it was a damaged beer, chalk it up as a loss and decide if you want to replace it or not. You don't want to raise red flags for yourself.
That's all that I can think of now, but that's a hell of a lot more than what was given to me when I started. You kind of learn things in time as to what is right, what is wrong, what is expected, what is not, how to package so things don't break, and most importantly how not to be a d!ck.