One big difference is the equipment. The lens focal length is typically 50mm to 200mm. The longer lens will give you more working distance between the camera and the subject. To get it to focus close enough to get moderate close-ups of the flowers, you have three general choices: use a macro lens, use close-up lens attachment, or use an extension tube. A macro lens is specially made for close-up work, and has the internal mechanics to focus quite close all by itself. Unfortunately they are not cheap, nor fast, and you may not use it for anything else. A close-up attachment is a convex lens that screws into the front of your normal lens like a filter. Nikon makes some high-quality ones that work well. An extension tube is a hollow tube that fits between the camera and the lens, and makes the lens focus closer. Even though they are just empty tubes, they still require extra exposure. An extension tube on a zoom lens is quite interesting--the focus control has little effect and you focus by zooming. If you want to get very close, you need to use a bellows.
Another big difference is the lighting. While wildlife and scenic photos look great with warm sunlight in the early morning, overcast weather is much better for flower pictures. The overcast gives soft diffuse light like a big soft box, with no dark shadows or glaring highlights like you would get with direct sunlight. Wildflower photography can be much less stressful on your body because you can sleep in late and go take your pictures in the afternoon when the clouds appear.
Achieving decent depth-of-field demands a small F-stop, which demands a
long exposure, which requires a tripod. Since most flowers are pretty low
to the ground, your tripod legs need to be adjustable so it can go down
very close to the ground. This may mean eliminating the center column.
1/30 sec at f/8
1/4 sec at f/22
Once you have your equipment all set up, photo composed, and your finger poised on the shutter release, you will meet the eternal demon of flower photography--wind. Since exposures will range from 1/30 second down to 1 second, you can't tolerate any wind. Unfortunately, the afternoon storms which bring clouds usually bring wind too. So you have to wait for the wind to stop, and sometimes this is a long time. Sometimes there is a period of calm after the rainshower passes by, then you can get pictures with drops of water on the flowers. You can use a piece of stiff wire to steady the flower in a light breeze--form a hook in one end, then poke the other end into the ground and put the stem into the hook.
Be selective when you choose your subject. Many times you are faced with a whole field of the same flower. If possible, choose one that has a large empty space behind it so the background will be far out of focus and less distracting. If you have multiple flowers, be sure they are all the same distance from the camera so they will all be sharp. Pieces of dead grass in the background are extremely distracting, so spend a little time and remove them. You may need to temporarily move other leaves or stems, which can be held out of the way with sticks or rocks, and released after you are finished.
You need to be roughly on the same level as the subject. Since the flowers are down on the ground, you end up kneeling a lot and trying to see into the viewfinder that is down low. Some flowers like to grow in marshy areas, so the ground is all mushy around them and you get your shoes and knees wet and muddy. Mosquitoes like marshy areas too, so they come and walk around on your head and sting while you're kneeling in muck, waiting for the last breeze to stop. That's when some curious people wander by and ask what you're taking a picture of. It is such glamorous work.