Some important notes.
Don't jump into higher difficulty games without having spent the time to have leveled up any class you are going to use to an appropriate level. You will simply cause things to be harder for the other players as you will be unable to cause sufficient damage to carry yourself, you will be unable to afford decent weapons and each additional player causes more and tougher zeds to spawn in each wave, which is a problem if you die early each round through being unable to keep up.
Assuming that you are reasonably skilled, aim for beginner 0-1, normal 2-3, hard 4-5, suicidal 6, hell on earth 6 + a good deal of experience.
Assault rifles and the firebugs mac10 have an alternate fire that toggles them from the default full auto to semi auto. You will almost always want to remember to switch to this. Combine this with using their sights and taking headshots, it may take you 2-3 bullets depending on weapon but you will almost always take down a pack much faster than just spraying around on full auto.
Everyone has a medic injector, USE IT. While it is best to use it on another player as you will be able to give two heal shots for the same recharge time, don't neglect to use it on yourself if you are currently away from enemies and are injured. Also when a medic is trying to heal you with his darts, dont keep jumping around. Aside from the husk and phatriach there are no ranged enemies so learn to ignore your instincts from other FPS's of needing to constantly keep dodging. This will not only allow your medic to heal you effectively from long range it will also help prevent zeds from constantly switching directions to follow you which make them harder targets for sharpshooters.
In my experience dual handguns are a liability as you loose the ability to aim accurately with the ironsights and have a much longer reload animation.
Skrakes (the chainsaw wielding zeds) are best taken out by a bezerker with a katana as each hit will briefly stun it and, as long as no one else is stupid enough to shoot at it causing the stun to break, it will be unable to respond.
At range a sharpshooter with a crossbow can kill them with a single headshot on lower difficulties and at higher difficulties will put it in a stunned state that lets you get a second shot to finish it off, alternatively if you have good aim the lever action rifle or m14 can take it out with multiple head shots.
Support can take it out with a few regular shotgun blasts then quick switch to the hunting shotgun and use it's alternate fire to finish it off. Half a clip fired from the aa12 will also put it down.
Demolitions, firebugs, commandoes and medics should avoid skrakes unles they have no choice, in particular dont blindly fire explosives at one as you will just make it much more difficult for your sharpshooter to get off a clean headshot.
Fleshpounds are best taken out by demolitions either by using a pipebomb deployed a little way in front of it and allowing it to walk over it or by scoring several direct hits with a M32. A LAW shot to the head will also work but is harder to pull off if it is headed for someone else.
Sharpshooters who have good aim and are at range can take them out with multiple crosbow bolts to the head. Note, it will stop and play it's enrage animation after the first bolt which gives you a chance to line up a second before it comes charging at you.
Support can take them out with a full clip from an aa12. At higher difficulties they will also need to use the hunting shotguns alt fire, and possibly start off with a couple of grenades.
Beserkers who have the timing down can deal with fleshpounds using the fireaxes alt fireand stepping back out of rangewhen the FP swings at you. This does take a good deal of practice and if you fail to get the timing right, or if someone enrages the FP it will result in a quick death.
Firebugs, commandoes and medics should wait for one of the other classes to engage before firing on the FP. Firebugs should use the mac10 if giving supporting fire on a FP as the flamethrower obscures the FP enough to make it more difficult for a sharpshooter aiming for a headshot. A fully charged husk cannon shot is an alternative option for dealing with a FP on lower difficulties.
A final note, Sirens should almost always be given the highest priority in being targeted aside from an enraged fleshpound. If one is able to get in and scream it can throw the entire team into disarray.