Time of Day - As with most photography, early morning has not only the best light, but often lower tempratures. Cooler weather has the butterflies sitting still longer trying to capture the heat. They prefer sunlight.
Weather - Cooler weather as I said helps. Also, just after the rain is a good time. They like to let their wings and will leave them more open at this point.
Food Source - Find a stand of flowers that attracts the species you prefer. Spray them lightly with a sugar water solution. If the species you like prefers fruit like mango, spray with a mixture of water and that juice. Don't oversrpay. You'll ruin the flowers.
Patience - Most butterflies startle easily at first, but if they fly away from that perfect flower setup, be patient. A lot of times, they will fly off for a minute or so and then be right back. Keep your camera focused on the flower and when the butterfly lands, you'll be ready for the shot.
Background - Prepare your stand of flowers ahead of time. Remove any distractions like weeds or debris. Use a soft brush to remove pollen or specks from the petals before you spray with any solution. Check from all angles to make sure there are no sticks or dead flowers in the background.
Props - If you decide to use something besides flowers, it may be more difficult to get them to land. In this case, try to make sure you have colors similar to the flowers they are attracted to. In butterfly nurseries, have your models wear pastel colors and again spray the shirt and hair with a flowery perfume or the sugar solution.
Similar tactics work for dragonflies although I don't think they care for sugar water. I hope this helps someone. It's what I usually do. Of course some places you can't do most of this, like a butterfly nursery. In those cases, just relax and do what is allowed. Most importantly, have fun. I find myself so amazed by butterflies I sometimes forget to shoot and that's okay too. LOL!
Photo credits: Diana Child.