There are lots of side effects -- probably as many as there are people.
The most obvious is that after receiving an enema you'll feel a strong need to expel it. Along with the introduced water will generally come other contents of the lower colon. Some people use enemas for this reason alone -- constipation relief. And the consequent side effect is that you won't need to defecate normally for a while.
Other side effects are minimal if the amount is moderate (1 to 2 liters = 1 to 2 quarts), the solution is plain water or plain water made slightly saline with salt or baking soda, the temperature is close to body temperature, the speed of water flow is not too fast and you use just a normal nozzle (don't forget to lube). If you put other stuff in the solution (soap, wine, ...) then it all depends on the quantity.
There will, of course, be sensations. I'm not sure I'd term these "side effects". Your abdomen may feel strangely full; you may feel the water flowing into or through your rectum or colon, you may feel stimulated (the lower body is full of nerves).
Beyond that, most side-effects probably have at least some psychological component. For some the water flow is soothing; for some the "knowing that I'm clean" is satisfying afterwards; for some their rituals of the enema are relaxing; for some (many here) the stimulation of an enema is a form of sexual stimulation. The same is true when someone else is involved -- domination, submission, intimacy, all depending on who is giving and who receiving the enema.
Let your body guide you (you can practice solo). An enema shouldn't be painful (i.e. sting), although there may be moments of discomfort. There is no "ideal depth" of penetration -- you'll need to experiment. Start cautiously, listen to your body, and read up or ask questions about specific issues as they arise.