How To Keep Your Teammates Alive

Cover in this case means: helping a teammate that is (about to be) in trouble due to attacking aliens. So basically: somehow stop the aliens before they hurt your buddies (any further).

If you have decent aim, you can already help a lot with certain weapons. Tesla, Autogun and Prototype Rifle work great, but the normal Rifle does, too. Pistols and sniper weapons require better aim, but like the K80 they can work wonders if combined with Adrenaline. Flamethrowers will cause some friendly fire but that's usually the lesser issue for someone surrounded by a horde. Just be ready to extinguish flames in case you accidently set someone on fire.

Sentry Guns are also great for cover if you point them at teammates instead of away from them (unless it's a Flamethrower/Explosion Sentry).

If you have an inaccurate and/or dangerous weapon (e.g. Grenade Launcher, Minigun), well-timed melee attacks can help against individual aliens and even smaller groups of swarm.

If you happen to play Medic (and you should, since it's the best class to keep teammates alive) with a Medgun, then practise healing teammates already while they are being attacked (and not after). Since you are defenseless while doing so, consider bringing Electric Charged Armor and use it before aliens can interrupt your healing. If necessary, scream like a little girl ask for cover via microphone.

Most extras have limited use, but some of them are very effective at covering.

-Freeze Grenades: A great all-rounder against any kind of alien threat. Just keep in mind that all is does it buy some time: the aliens still need to be killed before they thaw. That's usually enough to save your teammate from dying though.
-Hornets/Smart bomb: Very useful in confusing situations, but they deal minor friendly fire (which is usually not an issue)
-Electric Charged Armor: Cannot only be used for yourself: get into close range of your teammate and activate it to stun all nearby Aliens. Extremely helpful if a teammate is trapped inbetween Shield Bugs, but you need to get really close then. While this is active, you can safely 'defuse' all nearby parasites as they instantly die when attacking you. So make sure they do THAT instead of jumping on teammates.
-Adrenaline: Since it can be used globally, always keep an eye on your teammates' health-meters. If someone gets infested or suddenly receives a huge burst of damage, use it to greatly increase their chances of survival. It also makes things much easier when it comes to covering a nearby teammate with conventional weapons.
-Assault Jets: Not only can you bypass all swarm between you and the teammate in peril, but it also knocks back aliens at the point you land at.
-Blink Pack: Quite fast and stuns on arrival which can save a teammate. Can be risky for yourself though.
-Tesla Coil: Minor delay before it activates, but it lasts much longer than the other extras
-Flares/Flashlight: Very rarely used, but they can help rookies to spot parasites and swarm e.g. in the Syntec Residential vents. Flares' provided autoaim also helps a bit with cover.
-Power Fist: Also rarely used, can be useful to one-hit aliens in melee on higher difficulties. Combined with Tesla or Flamethrower this is actually a decent choice.

Hardcore Friendly Fire is a different case when it comes to covering: you can potentially deal more harm then good. Consider using shorter bursts: aliens will flinch when suffering some damage, which can already be enough to help your teammate. Tesla is obviously the savest way to cover, whereas Sentry Guns harm your teammates if Hardcore Friendly Fire is enabled. Power Fist can come in handy sometimes, but you risk getting yourself hit when closing in on a teammate.
Also, invent new curse words politely point out bad positioning to reduce friendly fire incidents in general.
Most lethal weapons are: point blank (Vindicator) Shotguns and Grenade Launchers (especially if the entire magazine is spammed instead of careful doses).

Some players might need more cover than others. Here are some examples/indicators:
-Players with a high ping (you can see the ping in the menu that has vote-kick and vote-make-leader)
-Techies while hacking (d'uh)
-Techies in general just because you probably lose the mission when they die
-Medics when healing (especially when healing parasites: you don't want the medic to stop healing in favor of self defense, if you can easily avoid that with some cover)
-Players with slow-reloading weapons and/or weapons that slow you down while reloading (especially if they don't have any backup weapon or extra to stop a horde)
-Players welding or setting up sentry guns (this is not as critical though as they can always stop to defend themselves)
-Players picking up ammo, making a melee attack, recovering from a jump-roll
-Players constantly using melee attacks against a horde of swarm (indicates they possibly cannot shoot for some reason)
-Players that are limited to one weapon and that weapon is one of the following: Grenade Launchers, Miniguns (before the spin-up is ready), Sniper Weapons, Teslas or (god help you) Mining Lasers
-Players currently injured (some characters have bonus health though) and/or infested (unless they use Electrically Charged Armor, in that case better cover the medic)
-Players knocked prone by a Shield Bug attack (until they stand up, they are basically stunned)
-Players using the turret-console in Rydberg Reactor or reading any of those porn story PDAs lying around
-Rookies (they often don't know where aliens attack from and sometimes panic when swarmed or infested)

Rookies are usually identified by their low level and/or lack of promotions. You can click their name and watch their stats to learn more about them (class experience, mission success rate etc.).
And you can just ask them: have they completed the training? Have they played their current class before? Are they familiar with their equipment or are they trying it out / getting an achievement? Have they played (finished) this mission before and know where to go/what to do?

As soon as you know what you are dealing with, you have an easier time predicting how people will (not) behave and if/how you can help them with some advice. Communication helps a lot, consider using a microphone ingame (and chat-text pre-game as it is usually easier to understand).

-Explain the mission to them. Drawing on the map in mission details map can be very useful here (make sure they actually look at it though). At very least, show them the route through the map. Most other things such as sentry-placement can be explained ingame, especially if you have a microphone. It can still be useful to point out hacks, unusual welds, infinite-spawn-areas which require rushing through and hold-outs.
-Recommend a loadout for the mission. Be open-minded here (different players are good with different equipment) but some general advice can be helpful e.g. some weapons might run out of ammo or make it difficult to fend of parasites, some missions have no doors to weld and so on.
-On Landing Bay (and Timor Station, although it's usually less time-critical there), explain how the hacking works if they didn't do it before

-As mentioned, they usually require additional cover
-Depending on their weapon and behaviour, teach them to be more ammo-efficient
-Point out imminent Spawns
-Point out the insta-kill pit in Cargo Elevator
-Remind people that they can dodge green projectile using the jump-roll
-When running into medpacks on the map, point out that they can pick it up, use it, pick up their old extra again (some people don't realise this)
-Have a look on their ammo: at appropriate times, remind them to pick up ammo and/or to reload
-If they reload with an almost full clip, remind them that the rest of the clip ammo is lost (this is usually only done by level 1 rookies who just started playing)
-Point out the dangers of fire and be ready to extinguish flames
-On easier missions and/or if things go well, it can help to let them make their own experiences in a 'controlled environment': this can even include not preventing them to be infested with a parasite in order to demonstrate the massive amount of damage and disorientation it can cause.
-Remind them of their grenades (especially stun grenades) and extras. You can see a teammates extra next to their health/ammo bars while pressing duck. A good example is the Electric Charged Armor, some people don't realise it has to be activated.
-Make sure the team does not split up too much (you should have seen enough horror movies and parasites to know better) e.g. rookies have a tendency to fall behind, especially since the popular-among-rookies Autogunners are slow and even slower when fireing.
-If you spectate them (when you're dead or joining late), don't forget to twirl your manly mustache give them advice e.g. where they need to go and where they can find ammo/medpacks (remember that you can draw on the map)