With the help of a couple of more experienced traders here, I discovered it wasn't that hard. I bought some 6x6x6 boxes at Walmart for less than a dollar apiece. I used some leftover bubble packaging I got when I had ordered a couple of things that weren't related to card collecting. Those bags that you get at Walmart and Dollar General work well for packing, too.
I use those little bags and put about 25 cards per bag, and then wrap them snuggly in bubble wrap. I then place that into the 6x6x6 box with more packing around it. This seems to work.
Another trader here uses those Small priority mail boxes. (At the post office, the clerk can point out which is the small.) On a recent deal, I was on vacation and wouldn't be able to mail my part of the trade until I got back. When I returned from my trip, his cards already had arrived, so I just copied the way he did it when I sent my cards to him. The cards went into the small bags and were tapped together. Then those plastic top-loaders were used to protect the cards on top and bottom. More packing when into the box.
I hope this helps, although I'm afraid I haven't described very well how I do this. I'm sure experience can help you figure out what works best for you.
I love to trade! Check the top couple of paragraphs of my profile to see my general trading desires. If you're uncertain if I’ll take a certain trade, message me and we can figure out something.