The first question is are these damselflies or dragonflies. They both mate the same way and are very similar. I believe these are damselflies, but aren't sure. They seem to have protruding eyes, which would mean they are damselflies, as dragonflies have flush eyes.
To mate, the male first grabs a female by the back of her neck with claspers at the end of his abdomen. The claspers actually fit into species-specific groves in the female. From here, the pair can fly around in tandem (this was not done by these two). If the female is sexually receptive, she will lift her abdomen to bring her "vagina" in contact with his "penis", allowing the male to transfer his sperm. While this is occurring they form a heart-shaped "wheel".
To mate, the male first grabs a female by the back of her neck with claspers at the end of his abdomen. The claspers actually fit into species-specific groves in the female. From here, the pair can fly around in tandem (this was not done by these two). If the female is sexually receptive, she will lift her abdomen to bring her "vagina" in contact with his "penis", allowing the male to transfer his sperm. While this is occurring they form a heart-shaped "wheel".