So this will be my first swap or shipping of beer, without trying to Google it on my phone, what is the best way to package safely?
Best way? Best I've seen was a box with Styrofoam specially made for the 6 bombers of awesome homebrew I got from an awesome brewer in Texas.
I individually wrap my bottles in bubble warp, and then pack in the box so they can't wiggle around. Line the box first with a garbage bag, then tie it off once all the bubble wrapped bottles and packing material is inside. In case of a leak, it contains it and keeps them from throwing it away.
Do not use the US Postal Service. I recommend a private shipper such as UPS or FedEx. I'll avoid the debate on rules and ethics, and just say that if they ask me what is in the box I tell them its "homemade gifts." I've also used "yeast samples" when shipping bottles of live yeast in bottles of spent wort to competions that receive their shipments at breweries.