For most of your outdoor close-ups you'll probably use the natural lighting on the subject. If part of your subject is in sunlight and part in shadow, you can use a reflector, such as crumpled aluminum foil or white cardboard, to reflect the sunlight into the shadow areas. Backlighting and sidelighting can be quite effective for making close-ups of subjects like flowers and foliage. These types of lighting bring out the texture and emphasize the translucency and delicate qualities of such subjects.
Many advanced photographers like to use flash for their outdoor close-ups.
Flash close to the subject allows you to use small lens openings to get the depth of field you need for close-ups. When using flash, it's a good idea to use the fastest sync speed available on your camera. Using a combination of a fast shutter speed and small lens opening with flash lets the background go very dark because there is so little exposure from the daylight. You can use this technique to tone down a distracting background or to make a bright, colorful subject stand out against a dark background. Shooting at fast shutter speeds also minimizes subject movement, such as the swaying of flowers on a windy day.