Bruising
Bruising occurs when blood vessels are broken under the skin and the resulting internal bleeding clots. The skin tone will start turning red or blue and transition to a deeper purple or black and then to yellow or brown over a few days as the body breaks down and removes the dead blood. While most of the time they don't, almost all modification and Body play procedures can and do lead to bruising from time to time. Anything from minor discoloration to immense surrounding bruising is possible. Minimize your chances of bruising by making sure you're fully fueled on Vitamin C, as well as by not taking blood thinners beforehand (Alcohol, Aspirin, and so on).
If the bruising is caused during the procedure and doesn't get worse, it's generally nothing to worry about, assuming you don't have a Hematoma that could go septic. If the bruising is not linked to a healing mod, but does appear to be linked to a healed one, it may be causing persistent irritation under your skin and it should definitely be looked at by a professional (you may have to remove it in this rare case). Bruises can take months to heal in some cases but are usually invisible within a few weeks. No special aftercare should be needed.
Below are some pictures and additional information on common bruising issues.
Types/Causes of Bruising
Bruising around fresh tattoos
It is not at all uncommon for fresh tattoos to have a "halo" of bruising around them for the first few days (although it certainly implies a heavy-handed artist). It won't affect the healing. (Associated images)
Bruising from suspension
Because suspension involves piercing and separating vascular skin layers, sometimes by force, bruising does happen, although many people experience almost none (in part because the force of the hook and the weight of the body put pressure on the wound). Bruising can be minimized both by first doing a thorough Massage of the skin in the area, which causes the layers to separate less traumatically. Burping and bleeding out the wound by massage afterwards will also minimize bruising. (Associated image)
Bruising from facial piercing
Eyebrow piercings often bruise — you know how easy it is to get a black eye! Other piercings can bruise as well, but in rare cases eyebrow piercings can lead to persistent bruising in some individuals, even long after the piercing is healed. In these cases alternate placement or removal may be necessary. (Associated images)
Bruising from the clamps
Sometimes a piercer will put the Clamps on tight enough to cause bruising, either because the person is especially susceptible, or because they simply put them on too tight. The bruising from this is temporary and nothing to worry about and won't affect the healing. (Associated images)
Bruising from nipple piercing
Bruising from nipple piercing isn't that common, but it tends to be fairly graphic when it does occur. In the case of males it's generally nothing to worry about, but for women risks are increased — the example shown below right could easily escalate to Mastitis if infection set in. In each of these cases below it would be a good idea for the person to visit their piercer to have them look at it just to be safe. (Associated images)
Bruising from other body piercings
Most bruising tends to be limited to the area around the piercing only and heals quite quickly. (Associated images)
Bruising from male genital piercing
Genitals are very vascular and can bruise dramatically. However, unless this bruising is also accompanied by water retention or excessive swelling it's typically not anything to worry about. (Associated images)
Bruising from female genital piercing
As with male genitals, female genitals are very vascular and bruise easily. Again, unless the bruising is persistent or accompanied by a lot of swelling, it's rarely anything to concern yourself with. (Associated images)
Bruising from heavy mods
While procedures like implants (the photo below shows a heavily bruised but inside-the-realm-of-normal Transdermal implant), castrations, Subincision, and so on are expected to bruise, often excessively, this bruising can also be indicative of underlying hematomas more serious than just what's normal. (Associated image)
Addenda
Above is illustration of the normal range of bruising you could see after various BME-related activities. Please note that a lot out — bruising is also not abnormal around Play piercing or even after heavy Vacuum pumping. Basically if bleeding can happen without that blood leaving your body, you're going to get bruising.