Anyone who has read World war Z will know that even after the war they still needed to clear the sea of zombies. While this is not a problem with fast zombies who will just drown, but when you get slow zombies they can survive for ages floating underwater.
Protection against injury while underwater presents a number of serious concerns that simply don't exist on the surface. The most prominent is the threat of drowning; any kind of viable armor is going to weigh significantly on a swimmer or diver, and any armor made of metal, such as chain mail (including bite-resistant suits designed for sharks) will make movement and propulsion more difficult. These particular types of armor are naturally fatiguing to begin with, as they hang off of the body even when strapped down, and would provide even greater resistance whilst underwater, compounding the fatigue caused by swinging the arms and a melee implement through water. Total physical exhaustion strikes quickly in melee combat, and is worsened by heavy protective equipment; these effects are only amplified under the surface.
Another concern to take into account is the simple mass of a suit made of metal; a swimmer or diver stands to lose buoyancy by adding only a small amount of weight to their person. Consider the ballistic armor worn by military personnel conducting maritime operations; such vests can weigh only a couple dozen pounds, and are largely fabric-based, but are designed to be removed the moment the individual wearing it falls in the water, so that it doesn't present a drowning risk. Any deliberate combat underwater (especially if one was implementing protective wear) would require scuba equipment of some description, as well as individuals familiar with such gear, and how to safely carry and use it underwater.
As mentioned above, scuba equipment would be a near necessity for conducting any kind of credible underwater operation, both for the longer duration of uninterrupted combat it would inherently allow, as well as simply reducing the risk of suffocation faced by individuals wearing protective equipment.
It should be noted that while firearms designed to be effective when used underwater technically exist, it cannot be stressed how exceedingly rare they are in all cases, even in countries that have adopted and issued such weapons to maritime special operations forces. In cases such as this, several dozens or hundreds of the weapons might exist in total; a production run might include enough weapons to arm a select number of a given unit that has need of such a weapon, and a few contingency weapons to be held in the unit's armory and training apparatus.
Many normal firearms and their ammunition, contrary to popular belief, can in fact be used underwater. However, several caveats are evident. The differences in pressure may cause the weapon to fail to cycle, requiring manual operation of semi-automatic designs. The greatest concern is that normal ammunition fired underwater doesn't actually travel that far, or with very much force past extremely short range. Due to the physics at work, most rifle cartridges lose nearly all lethality after traveling a single meter. Handgun cartridges by and large can perform slightly better here, but are typically still limited to ranges of less than three meters.
Perhaps the most effective weapon available to civilians is the spear gun; most commercial models enjoy a range of six to eight meters, though the ones capable of propelling a spear eight meters are very large and bulky indeed.
Though it is difficult to break down specific individual tactics and procedures that may be employed by civilians in this scenario, it can certainly be recommended that melee combat be avoided at all costs. Especially underwater, there is literally nothing to be gained by attempting to engage your enemy in hand to hand combat if that is only range in which your enemy poses a threat. Also, coagulated or not, bodily fluids and tissue would present a severe infection hazard in water if one were to begin ripping at an infected individual (there's a reason that individuals with open wounds, infectious diseases, and mucus discharge aren't allowed in public pools; it poses a risk of infection, especially when considering a disease spread by fluid contact).