I dealt with my first swarm this a few days ago. After freaking out for a good 10 minutes, I grabbed a minnow bucket, because I had no other container available, put on my veiled jacket, grabbed my bee brush and brushed them into the bucket making sure I got all I could. Doing this more or less ensures you have the queen. Once I set the bucket in the shade and saw bees clinging to the top of the bucket I knew I had the queen.
I didn't have an extra hive ready to go, so I had to use what I could. I slapped together a bottom board, set a super on it, put in some frames and shook the bees into the hive. I pulled an inner cover from another hive and covered the hole with a bee escape. On my next free day, I plan on making nucs, so I won't get caught with my pants down again!
So, the major thing is to have a nuc, or several, ready to receive a swarm. You can use any container to put the bees in to get them to their new home.
Hive them and add feed like you would a package.