Did someone say 'zombie'?
What would game developers do without zombies eh? Halo's version comes in three flavours; combat forms, carriers, and spores (more correctly called infection forms).
The combat forms are the ones with weapons, flailing arms, or whipping tendrils. They're the main ones to watch out for of course, particularly the ones with rocket launchers! The pistol is great for whittling them down at distance; the shotgun is great close up. But don't overlook the plasma weapons, both of which are far superior to the assault rifle against Flood; see the Flood onslaught challenge for related discussion. As long as you're not too close, the needler works fine too. Melee attacking can do a little damage, but you'd probably only want to resort to that in an emergency, such as when you've just run out of ammo and reckon that a whack or two will be enough to finish the job.
A downed combat form may reanimate after a few seconds (unless downed by an explosive blast - typically a grenade or rocket, or a popping carrier), but it doesn't usually take much more to finish the job for good. Actually you don't need to wait for reanimation to finish him for good. Pre-emptive firing into the seemingly lifeless body works just as well; or you could've added extra fire when he was going down in the first place.
The carriers are the bulbous waddling fellows that like to explode up against you, releasing between 3 and 6 spores (with equal probability I think). Judging by their little legs, it looks to me like they used to be Grunts. These guys move quietly, and in the heat of battle you have to be careful that they don't come up behind unnoticed, else the bang may be the last thing you hear. They're essentially walking bombs, and you can use that to your advantage by popping them among other enemies. The pistol is the ideal weapon for picking them out from a crowd, but try to avoid having a carrier blown your way. If a group of them is waddling towards you, go for the frontmost one so the others get blown away from you. Except, still watch out because these guys bounce off walls!
The spores are the scampering little bubbles that want to nibble you. More correctly they're called infection forms, while Flood spores are instead something released by an infection form, causing the infected host to mutate. But a lot of people including myself have come to call them spores and I've elected to continue doing so. I'm partly taking the view that as a trooper in the field - which is my main psychological standpoint - I'll leave the science stuff to the boffins. Me, I just shoot stuff, and I've always known these pests as spores.
They tend to flock in packs, and occasionally ambush you in great numbers. But the only real danger they pose is that in the heat of battle against combat forms, you might fail to notice that a lot of spores are nibbling, causing significant damage. You'll feel a right fool when you collapse lifeless to the ground, covered in miniature assassins. However, if you make sure to continually move about, most spores that jump at you will miss, potentially enabling you to ignore them for a while until more urgent threats are dealt with.
Eliminating a mass of spores is pretty easy because if you pop one it usually causes a chain reaction that pops a few more. So, a few shots from almost any weapon can quickly wipe out a group; there's no particular need for spraying fire all over the place. You can also simply use melee attacks; just keep backstepping and whacking spores on the ground or as they jump at you, and the group can be thinned out in a few seconds. However, the higher the difficulty level, the more resilient spores become against chain reaction popping. On Easy, popping one spore in a big group could wipe out the whole lot. On Legendary it's a completely different story. Chain reactions don't propagate anything like as far, and it takes a lot more work to wipe out a group with gunfire or whacking. A grenade can still do the job quite nicely though!
Here's a tip culled from bitter experience. Never use a rocket launcher when there are spores around jumping at you! I'm sure we've all been there.
Bait and retreat
With many Flood encounters, the safest tactic to use is 'bait and retreat'. Attract their attention to draw them into an attack, then retreat and whittle down the stringed-out mob from a safe distance, ideally with a pistol (you can also lob grenades into their path of course). Being a pistol fan, this is a favourite tactic of mine in 'The Library' when I'm in no rush to get through. The enemy rarely gets close enough to even take a shot. A secondary virtue of stringing out the enemy is that fewer of them have a clear line of sight to you, so will be unable to fire effectively even if within range. Particularly when up against a small group, it can be worth deliberately moving around so that the frontmost attacker blocks the line of sight of Flood coming up behind (a tactic you can equally use against the Covenant of course).