1. Take your photographs on a cloudy day.
Sure, its easier to get outside when the sun in shining, but an overcast sky can provide some of the lushest light for photographing flowers, allowing the greens to pop and the colors to saturate better than they might on a super sunny day.
2. Frame your flower up close.
You may want to slow your visual world down and focus on a single bloom. In this case, choose a shallow depth of field and get in as close as possible to your subject. On an SLR you will have multiple options and and even different lenses you can use to accomplish this. If you are working with your cell phone you can use automatic features such as macro or portrait mode to accomplish the look you are going for.
3. Make use of backlighting.
Photographing flowers with your light source directly in front of you can cause translucent petals to appear as if they are glowing. The best way to access this type of lighting is to take your photographs in the late afternoon or early evening when the sun is low above the horizon.
4. Photograph your flower indoors
If you can bring your blooms indoors you can manufacture the perfect lighting environment to highlight exactly the aspects of the flower most important to you. When I am shooting my flower crowns for online content I use a light box and a sweep (a piece of poster board attached so that it curves behind the object and prevents a seam or background edge from appearing in the photograph.
5. Edit your photographs.
There are dozens of easy to use photo editing programs and apps available online. My favorite in Snapseed (its free!). This simple app can do so much and is fairly straight forward to master. When I have a photo I want to share on social media I almost always take a pass at it on Snapped first. My favorite tools are lens blur, which helps mimic a shallow depth of field and allows you to decide which portion of your photos is in sharp contrast while blurring the edges of the rest. I also love the brush tool which allows you to pinpoint areas that you want to highlight by making them brighter (increasing the exposure of a section) or saturation for areas you wish to deepen the appearance of color.