1. First, let's look at the nuts and bolts of exposure. I find that a fairly high ISO in the 800 to 1000 range allows a very fast shutter speed and a medium aperture. The reason you don't want too wide an aperture is that you want to maximize the depth of field—which is inherently shallow when working closeup with small objects. The difference between f/4 and f/8 might be the difference between a specimen that's entirely in focus and one that only has part of one wing usably sharp. And to get a fast shutter speed at f/8, you may need to boost your ISO accordingly. I want a shutter speed of at least 1/500th, and preferably over 1/1000th. Adjust the ISO as necessary to achieve this, or consider using Auto ISO to allow your shutter speed and aperture to remain where you want them
2. As for equipment, a macro lens is obviously immensely helpful. I couldn't have gotten some of the beautiful extreme close-ups that I made without my 100mm macro. (The fact that it has built-in image stabilization is also helpful for handholding, too.) While the macro is useful, it's not mandatory. Some of the nicest shots I made were with a plain old 24-70mm zoom. I even used this lens at the wide-angle end to help show context. You can still focus close and make nice compositions that incorporate the environment—especially if it includes colorful flowers or interesting foliage.
3. Don't waste your time trying to catch butterflies in flight. Let me rephrase that; I'm happy for you, if you want to attempt this, but don't expect this method to yield very many usable images. Butterflies are so fast, with very quick, fluttering changes of direction, that you end up shooting frame after frame of out-of-focus images. When you do happen to catch one in flight, I've found it's hard to tell they're flying—they look just like the do—alighted on a flower or perfectly at rest in midair. But remember: no risk, no reward. If you pick an optimal location and let your motor drive fly—and can muster a bit of good luck—you just might catch a beautiful in-flight shot that blows away the basic butterfly photos. My point is that the in-flight process can be very frustrating, so concentrate your energy on finding beautiful butterflies at rest in beautiful locations. This is challenging enough.
4. Look for edges of light. The transition areas from sun to shadow are great places to make photos, especially when you can get a subject lit against a background that's shaded. In the case of this subject, a brightly colored butterfly will simply glow when illuminated against a dark background. The nice thing about photographing butterflies is you can do it in any light—soft and diffuse or direct specular sunlight. The key is to keep your shadow out of the shot, because in soft light it will make the exposure very low, and in hard light it will make for an unsightly shadow in the frame. Working on the edges of light will also allow you to try interesting scenarios such as backlighting and edge lighting to help make the photo really pop.
5. Target color. If you can't find the most colorful butterfly—or even when you do—look for colorful surroundings in which to shoot. That could be next to a bright yellow flower as the butterfly is feeding, or maybe perched on foliage the seems to glow with rich purples and reds. Butterfly photographs are so much about color, don't forget that you can find it in the background, too.
6. Speaking of composition, start by choosing a position where your sensor plane is close to parallel with the butterfly's wings. With open wings, that means you're likely shooting from directly above—rather than from the front or side. With closed wings, you'll choose a side-angle position. These angles not only help keep the entirety of the wings usably sharp, they help you approach the butterfly from its most photogenic angle. You also want to try to show all of the butterfly in your shot. I can't tell you how many times I've made a great image of a butterfly, but just barely missed getting one wingtip in frame. It can ruin the entire composition! To be safe, you can shoot wider and crop in post. Of course, rules like these are perfect for breaking—like when composing from head-on. From this position you're likely not going to show the entire butterfly in your photo and you're probably not going to see much of the wings. But, what you'll have is an interesting frontal view of an interesting little creature. And, as with anything, looking it in the eyes is inherently interesting.