#1. Butterflies seem to be the most active when you're heading out of the house on your way to run some errands or after you've prepared yourself to do some work in the garden. You know, those times you don't have your camera handy. Keep you camera near the front door so you can reach for it if you spot butterflies in your garden. Make sure your memory card has space and your battery is charged.
#3. Make yourself shorter. I'm not particularly tall but I've observed that my shadow will cause many a butterfly to flutter off even before I'm near enough to actually be a threat. I'm no expert, but my hypothesis is that it is some kind of evolutionary adaptation of the butterfly to avoid getting eaten. What causes shadows from above? Birds. What eats butterflies? Birds. Crouch down to avoid casting a shadow that will scare off a butterfly before you manage to take a photo. If you can't crouch down or are embarrassed to be seen crawling around the garden, approach the butterfly so that it is between you and the sun.
#4. This brings me to what I've found is the best times to take butterfly photos. Cloudy days and early in the morning and evening seem to be ideal. Butterflies need heat and sun to fly. Get to them when they are at their slowest.
When the sun is at its highest point in the sky the butterflies are warmed up and the light creates harsh shadows which darken details. Use a bit of flash if you're taking photos around mid-day to keep some of the details in the shadow.
5#. Finally, take a lot of photos in rapid succession. The more photos
you take the greater your chances are that you'll get one of the
butterfly that is in focus and you'll be happy with. If a butterfly flies away I'll stay in the same spot and wait for it to return. There are no flowers to speak of on either side of my garden so they go up, circle around and usually land a foot or two away from where they were when I scared it off.
Years ago I was a member of a photography forum and there was this woman who took the most amazing butterfly photograph I had ever seen. I asked her what her trick was and she told me that she captured the butterflies and placed them in the fridge for about 30 minutes (see #4) and then would take them back out into the garden and place them on the flowers. With the body temperature of the butterfly lowered she had plenty of time to get in nice and close and take as many photographs as she needed before they warmed up enough to fly away.