The soft even light of an overcast day compliments the delicacy of the flowers and there are no shadows and no harsh bright spots, which makes it easier to get a good exposure.
Bright afternoon sun creates hard shadows and takes away from the natural beauty & softness of the subject.
On cloudy days, or during the golden hours, the lighting is much softer & will be more even throughout the photo.
Backlight happens when the sun is directly in front of you lighting your flower from behind. Because flower petals are translucent, backlight makes flowers appear to glow.
Try to capture backlit flowers late in the day when the sun is close to the horizon which will cast nice warm light on the rest of your image too. You might even be able to catch some rays of light filtering through the trees.
Use a telephoto lens and zoom in to the flower. Take note of the minimum focussing distance of the lens, for example, a 70-300mm telephoto lens has a minimum focusing distance of 1.5 meters (or 5 feet). It simply will not focus on anything closer.
Use extension tubes which are hollow tubes that you place between the camera and the lens.
Use a dedicated macro lens which has the ability to focus on objects that are close to the end of the lens.
Use your feet. Get in there!
If your subject is in the shade, you can use a reflector to bounce some light back towards your subject and make the flower more vibrant. Also try using your phone's light or camera flash as as a fill-flash.
As with every photograph, the background can make or break the image. Try to change your position so that there is nothing distracting behind your flower.
Shallow depth of field is when only part of the image is sharp and the rest is soft and out-of-focus. You can achieve this by using a wide aperture (low aperture number) such as f/4 or f/2.8. The effect is even more pronounced if you are using a telephoto lens with a wide aperture.
If your flower isn’t sharp, try using a faster shutter speed. Check your focus -- if necessary use manual focus to ensure the camera is focussed on the most important part of the subject.
Move around, try some different angles -- photograph the flower from behind or underneath to capture an unusual point of view.
Try positioning yourself so that another flower is in front of your main subject and very close to the end of your lens. The secondary flower will become a blur of color and your final image will have a more abstract feel.
With a handy spray bottle of water, you can create dew drops for spiderwebs, leaves, flowers, and everything else you choose to photograph. Colors will become more rich and saturated (is this where the term came from?), making for more vibrant and rich-looking photos.
Spray the front element of the lens with just a bit of mist -- creates wonderful bokeh and light effects which can really add a lot of interest to an image.