Halo's two types of grenade add hugely to the fun of combat. On the one hand you've got the UNSC's frag grenade, which explodes shortly after coming to rest, and which can be bounced off surfaces, such as off a wall to reach an enemy around the corner. On the other hand you've got the Covenant plasma grenade with its delayed fuse and fiendish sticking ability that allows you to 'tag' enemies or enemy hardware. When you add the phenomenon of chain reactions to the equation, and factor in the superb physics modelling and explosion effects, and the comical way enemies react on being tagged, or fly screaming through the air after being blown sky high, you've got all the ingredients for some truly entertaining and spectacular fun. It's a tremendous job by the Bungie folk.
Frag grenades are relatively rare, so it can be worth saving them for when you either want to exploit their bounciness or quickness to explode. Plasma grenades are usually plentiful of course, being dropped by Grunts and Elites when killed. You'll pick up a steady supply, so there's rarely much need to ration yourself with those.
Faster lower throws
To make a grenade travel faster, run forwards as you throw it. This also allows the trajectory to be lower, makes aiming easier, and gives an enemy less time to dodge if you're trying to land a plasma grenade on them. It also lets you send a grenade further, if you're attempting some long-range mischief.
Shovel those grenades
Particularly in close-up battles against enemy that start to arrive in large numbers, it's generally a good idea to use lots of grenades. Keep an eye out for nearby plasma grenades to pick up, and if you're getting low, consider rushing in amongst Covenant dead to stock up again, even if you're going to come under a bit of fire for a while. The more you keep stocking up, the more you can throw.
In situations where the enemy tend to funnel into one spot to attack you, the tactic of 'grenade accumulation' can be used. Here, you deliberately leave plasma grenades accumulating among the dead, then lob a grenade to set the lot off in one colossal chain reaction blast when more enemy have funnelled in. Very satisfying.
If you have no grenades, a second tactic when faced with an arriving group is to deliberately let a Grunt start throwing a grenade, then kill him on the spot so he obligingly drops it among his pals.
Not behind them!
Beware of the danger of landing a grenade behind the enemy. The blast will blow the enemy towards you, and sometimes that will also bring a loose grenade that explodes as it passes. Not good. For similar reasons, it can be dangerous to lob a second grenade towards the enemy before previous ones have gone off (it's probably also a bit wasteful).
When a Grunt or Jackal has support coming up behind, consider landing a plasma grenade on him rather than finishing him off. He'll head back into his mates taking your fizzing blue friend with him to spread around. In particular, when enemies are funnelling in from an approach, this tactic enables you to get to enemies you can't even see yet.
With this tactic in mind, it can be advantageous to deliberately let a Grunt advance so he's nicely set up to become such a 'Grunt bomb' as I like to call them. To make it easier to land the grenade on him, stun him with a shot first (which may also cause him to turn tail). 'Jackal bombs' are just as easy to arrange if you've got a plasma pistol handy to stun him with a plasma ball that takes down his shield. Alternatively, ping a shot off his shield and he's likely to do a roll which briefly exposes his body, letting you do the tag.
Buying time to reload
In pressured situations where you're trying to hold back one or more enemies, throwing a grenade in the path of their advance can give you the time you need to duck back under cover and reload. If they don't have enough sense to stay back, they'll regret it. I'd normally use a plasma grenade for this.
Stalling an enemy's movement
If you throw a grenade trying to blast an enemy who's on the move or who starts moving, and you see that they're probably going to be out of the blast radius, you can often halt their movement by firing at them. Hopefully this will stall them long enough to get the full benefit of your explosive gift. Which is nice, yes?
If you want to get an enemy to turn around briefly to make them more vulnerable to an attack, try this. Lob a grenade so it'll explode harmlessly on the other side of them, then duck out of sight. When the bang goes off, the enemy is likely to briefly turn around to look, which is your cue to pop back out and attack. In particular this tactic could be used for getting Hunters to turn around so you can snipe them in the back from distance. It could also help reduce the amount of plasma you take in an attack on a nasty Elite.
When you're unsure of the exact location of one or more dangerous Elites ahead, you can try throwing a grenade somewhere. Often this will cause an Elite to utter something, even if the grenade isn't close enough to be a threat. That can give you a better idea of where he is, to help you tackle him.
Great practice in the rockslide megabattle
I can highly recommend the rockslide megabattle for improving your grenade skills and employing all the tactics mentioned here. It did wonders for me at least, letting me get far closer to the fluidity that a real throwing arm would give. Due to the intensity, you get far more practice than in normal play.