Hello feeble popgun
Fast melee attack aside, the assault rifle has to be the weakest weapon going. So weak that you might even consider it one of Bungie's few errors of judgement. With terrible accuracy, low stopping power, and an ammo clip that disappears in a moment, I've often felt you'd be more effective hurling loose rocks and abuse. It's nowhere near as strong as a plasma rifle. If I'm seriously interested in staying alive, I'd generally try to exchange it for something else at the first opportunity. I suspect that a lot of people playing on Heroic or Legendary would have similar opinions; and especially on Legendary, bearing in mind the murderous rate of alien fire.
It seems so odd that Bungie allowed this situation, because the assault rifle is meant to be the mainstay of the Earth forces. But its weakness effectively means that on the higher difficulty levels, if you want to fight the Covenant on a level playing field then there's nothing suitable that goes "badda-badda-badda", which is terrible. I know Bungie threw a good part (or rather, a bad part) of the FPS rulebook out the window, but the importance of having a decent adrenaline-pumping machine gun cannot be overestimated.
That said, on Heroic I've now grown to enjoy the assault rifle hugely. I realized that you can use it effectively, though you do need to be disciplined about it. Using the assault rifle is also a good way to deliberately make things harder for yourself, to increase the challenge. So let me pass on a few tips to anyone interested in giving it a second chance. I can recommend the rockslide megabattle as a fine practice ground; see Joys of the assault rifle in the 'Plateau front defence' plan, for what I consider the best AR fun in the game.
Short bursts please
A well known tip is that unless you're really close, you should only fire in short bursts. The longer you keep the trigger down, the wider the bullet spread and the lower the chance of bullets hitting the target. You can see just how quickly the spread worsens by doing some testing against a suitable wall and inspecting the pock-marks afterwards. Try half a dozen very short bursts at the same place. Now take a few steps right and try a single long burst on a fresh bit of wall, firing a similar number of bullets overall. After seeing the difference, you'll realise why short bursts should be your number one tactic.
Another good reason for efficient short bursts is to reduce the frequency with which you have to reload. This becomes a serious consideration in close-up battles where you're really being pressured. In the time it takes to reload, the enemy can push forward out of cover and begin to swamp you. When faced with multiple enemies, one thing you can usually do is make the Grunts run by quickly putting a bullet or two into each of them. This lets you conserve your clip for use on the more obstinate enemies, and may save you having to reload under fire.
Even more efficient than short bursts is what I call 'staccato' firing, in which rounds are fired separately by rapid twitches of the finger. This is far more economical than using bursts, yet has a comparably rapid effect once you get the hang of it. In effect it gives you a very slow machine gun but with relatively high accuracy. It also greatly reduces the frequency with which you have to reload, which can be an important consideration when faced with multiple enemies. For a good example of that, see the Flood onslaught challenge. It also conserves ammo, if that's a worry. In routine gameplay I often use it against Grunts beyond short distance. Most bullets will hit, and a Grunt goes down about as fast as with short bursts; or possibly faster when he's at relatively long range.
Taking down Elites
Now suppose you're up against a red elite with a plasma rifle. If you're already close up, you've got the opportunity for a 'charge and whack' assault; i.e. drill him with bullets as you close in, and use one or more melee attacks when you get there. If you're too far away, you can instead whittle down his shield bit by bit, using patience and movement. Pop out from behind cover just long enough for a few bursts, then get back under cover before he's through your shield. Repeat this a handful of times and he'll eventually go down, whereas you should be in the same good health as before. In the case where you're both out in the open, you can use the assault rifle's greater range to whittle down his shield.
Should you aim at the head? I imagine headshots do more damage, but the weapon has such low accuracy that most of the bullets would probably be whizzing past his ears, which wouldn't help much. Personally I stick with just aiming at the body to get the most hits.
When you're really close up, you can just let the bullets pile into his body and rely on the high rate of fire to bring him to his knees. Your proximity may tempt him into a melee attack, but that's fine as long as you're ready for it. In fact it's probably worth trying to tempt him, because it stops him sending piping hot plasma your way! Whilst he's busy missing a swipe as you cooly sidestep or backstep, you're continuing to pile in the shots. By about now he should be almost down; a good time to finish him with a brisk whack to the mandibles.
Where am I going?
Uniquely, the AR includes a small pointer in its electronic display, which apparently indicates the direction of the gas giant, Threshold. You can potentially use this to monitor your bearings and avoid getting lost, though I have to admit that I've never actually done so. In practice you soon get used to the levels of course, making the indicator rather superfluous.