Getting closer to a subject to focus on the details that are normally missed can make for an inspiring and intimate photograph. We are surrounded by things that can be turned into works of art just from looking at them from another angle.
Focusing on these flowers makes them pop out amongst the rest of the garden with similar looking blooms.
If there is a background visible behind your subject, try to make it as plain and unobtrusive as possible. This can usually be done with a low aperture. Since you are shooting so close to the object, the background will probably come out blurry anyway. High quality lenses can be used to produce stunning bokeh. Be sure that the background doesn't distract from the main elements in your close up.
Your camera's position and zoom can affect the perspective of your photo. To give the shot depth, move close and zoom out. Sometimes this will make the center is bulging, so be careful. Similarly, to flatten the perspective, move out and zoom in.
These flakes on a tree came out blurry, it's important to check with your LCD screen if possible to see if the details are as crisp as you wanted before moving on.
Even when you use a tripod and remote cable, or self timer the image can come out blurry. With close up and macro photography the camera needs more light to get the subject in detail. The shutter has to stay open longer which leaves your image more vulnerable to being damaged by movement. If you think you have everything perfect and that the camera isn't moving at all, double and triple check your focus. Try kicking it back or forward, then zoom in on your camera's LCD screen to see if anything changes.
Remember that review of the LCD screen is a small guide. When you upload the photos later you may find that ones that looked absolutely perfect are blurry when they hit the screen. Try taking as many photos as you can of your subject. Zoom in, zoom out. Move close, move back. Change the depth of field. Play around and take as many as you can. When you load the photos and pick out your favorite, look at what the settings were. After awhile you will notice the settings or the 'feel' of the photos that that catch your eye more than other techniques you have tried.
There are also macro lenses and filters available that can help you get super close shots. A quality macro lens will let you get super close and not have the blurry bulge that can happen with some filters.