All StarCraft Zerg strategies that deal with Zerg v Zerg matchups revolve around constant scouting and quick responses.
Scouting Use your Overlords to scout out where your enemy is located.
On 1v1 maps you will know where your enemy is before starting the game.
You should still send your Overlord over there because you will want to know what he is doing.
Keep in mind that he will most probably do the same thing.
In this type of matchup it really boils down to whether you want to play aggressively or you want to expand quickly and overwhelm your enemy.
Responding to your enemy's movements When you're more of a reactive player you will want to scout at all times, with all manner of units.
In some cases you will have to sacrifice a Drone to scout with it.
But this will be a very small price to pay for knowing when your opponent is attacking.
Usually in Zerg v Zerg games both players will try to rush each other with some combo of Lings and the one who is the quickest and who micro manages his units best will probably come out the winner.
If he doesn't kill his opponent outright he will, at the very least, do some damage to his economy.
On the other hand, if you see a Baneling Nest in his base, then you can be sure he's planning to rush you with a combination of Zerglings and Banelings.
In this case you can quickly put down a Roach Warren and get a couple of Roaches out before he attacks.
Once your Roaches are ready make sure to block off the ramp with them.
They are Armored and have a lot of hit points - they work great as blockers.
Once you see his attack coming, this is where micro managing is crucial.
You need to use your Roaches to snipe the Banelings before they get too close.
Ideally you should also have a couple of extra Zerglings around to deal with the enemy Zerglings.
It takes a lot of Banelings to bring down a Roach.
Banelings however, also do splash damage so make sure that your Roaches aren't clumped together.
After you resist this first attack, create a couple more Roaches.
If Zerglings are continuing to pour in you can be sure in your decision to put down a Spire and start making Mutalisks.
Two or three Mutas will be enough to harass his ground army enough to hinder him.
Better yet, you can fly to his base and eliminate his workers.
Once you started laying waste to his base from the air, you can also move on him on the ground with your defensive forces.
If your opponent goes air, then you will have to get your Hydralisk Den up as soon as possible and get some Hydras out.
Placing a few Spore Crawlers in strategic places wouldn't be a bad idea either.
Of course there's the very high probability of your opponent opting for Roaches as well.
In this case, the best way of countering him would be to build Roaches but also make some Banelings.
In a one-on-one fight, any advantage can tilt the scales in your favor.