Here's my ha'porth:
Inevitably, when you start, you'll ask questions like, 'what is it?' and 'how can I get close enough for a good photo without it flying away?' This is fun, the learning curve is steep and you'll have a great time.
But to my mind, the much more interesting questions are, 'what is it doing?' and 'why?' To answer these, you don't pursue but sit back and observe (preferably with a flask of real ale, if you are of an age). Chased butterflies are often little more than missed photo opportunities. Watched butterflies are lessons in living. Learn to see when a female is ready to lay, and then watch her painstakingly work over an area, hunting out exactly the right place to deposit her precious load, even though she will never see her offspring. It is a labour of altruistic love, undertaken with infinite devotion. Watch how males of different species defend territories in different ways. This spring, for instance, you will see commas sparring for sunspots that they will hold, if they can, for as long as it takes to impress a female. You will see orange tips roding round and round the same loops, stopping on the same flower heads as they do it. Watch different wooing techniques - which vary from sophisticated courtly dances, through dive-bombing instant chat-up lines to what can only be described as rape (some male blues go for it while the female is still drying her wings before her first flight).
Back to photography: for about thirty years, I've had a strict rule. I always stop pursuing a butterfly if I put it up three times. If it flies - because of me - three times, I let it go and just watch it get on with its life. All my photographs are taken on that principle, except in a very few cases of rare and/or difficult butterflies where a good picture is necessary for the record and I haven't got a net for photograph and release (in Switzerland, nets are sometimes necessary and less invasive than chasing).
And finally - you did ask for advice

- I've seen people trample and kneel on and lie down on vegetation and flowers just to get that perfect photograph. Ideally, in my view, there should be no evidence you were even there. I know some people think I'm too much of a purist on this, but aiming high is always good, even if the ideal is impossible in practice.
That's enough (solicited) advice!
Guy