Dancing with different partners
Because swing is a social dance, one should seek to dance with as many different partners as possible, rather than focusing on a single partner. Even if a lead and follow came to the dance with each other, it is disfavoured for them to spend the entire night dancing only with each other. In the United States, it is typical to dance one song in a row with a partner, two songs in a row if the experience was particularly enjoyable. In Europe it is often considered rude to dance only once consecutively with a particular partner.
Asking for a dance
Although traditionally a lead asks a follow for a dance, followers are encouraged to do the same. The person may either accept or reject the dance request. If the person rejects the dance, whether they might not feel like dancing or are reserving a dance for someone else, or they might be tired or just shy, thank the person anyway and ask someone else to dance. It is considered rude to decline an offer for a dance and then dance the song with another person -- unless you mention that you had the dance reserved and promise a later dance to the asker. To begin the dance, the lead should escort the follow onto the dance floor, with an arm behind the follow's back (though this is done less and less, and not at all in many scenes).
After the dance
A lead or follow should thank their partner for the dance and, if desired, ask for another. If there is a live band, they should also be applauded for their performance. Traditionally, the lead should then escort the follow back to their seat; however, this tradition is not widely followed for various reasons, to the point that escorting a follow off the dance floor might be seen as unusual in many dance venues.