If you possess an SLR camera, then because of its versatility, you have the ideal tool for getting up close and personal with invertebrates and most smaller variety subjects.
There is a choice of lens options available for this line of work and without going over the top, the Macro lens, either 50 mm, 100 mm, 200 mm, etc., would suit well. Or for even closer work, you may need the addition of close-up lenses, extensions or bellows.
Some electronic flash facility would be of some assistance.
For a better arrangement, it is possible to set up a bracket attachment for your camera with a flash unit on each end. Also excellent for photographing fungi and lichens.
A sturdy support is essential. One that will do just about anything and go just about anywhere, because now, you'll really be getting down and dirty, so your tripod must be reliable yet pliable.
A remote shutter release is also essential for eliminating camera shake, or you could use the camera timer facility.
With close-up photography, it is particularly essential to have a good understanding of the correlation between shutter speed and apertures, not only because of close-focusing but extremely narrow depths of field.
When photographing flowers and small subjects, a slightly overcast, but bright sky is ideal, as it eliminates shadows and bright spots on subjects.
You will also find the odd reflector will come in handy. To make a simple one, just crumple up a piece of foil wrap, uncrumple it again and wrap it around a piece of cardboard or something and 'voila', there's your reflector!
What do I use for magnification? For my current camera, I use a Pentax K5 2s. I also have a Pentax 100mm Macro Lens and to get closer, I have a set of three Hoya screw-on diopter, or magnifying filter/lenses. The set has +1, +2 and +4 magnifications. I usually start with a +4 and then add others if necessary. Normally I would remove any other filter I may have on my lens, such as UV or polariser because I just don't fancy the idea of all that extra glass. It promotes the possibility of lens flare and the quality of your available light can suffer. As your 'DOF' is very limited in close-ups, try to keep the plane of your camera parallel to the subject plane. That way you will be able to get more of your subject in focus.
You will notice, as you manually manipulate the focus control, that different parts of the subject will move in and out of focus and with your aperture set at its narrowest permissible opening (largest number), just how little DOF you have to work with.
If you're photographing the stamens of a flower, for instance, concentrate your focus on them, till you see every fine detail. Keeping the throat of the flower just out of focus in the background.
With close-up photography, you can either spend a lot of money buying the 'proper' equipment, or you have to make the most of what you have at hand (beg, steal or borrow), but I'm sure with practice you'll soon be coming up with some fairly good results.