Corners are a bit of a mixed bag in FIFA 13. There is no definite way to score them and it is sometimes a bit of luck. However, there are certain factors that you can control to increase the likelihood that one of your targets will get a head on your cross and score. If you take the corner well by following the rules below, FIFA 13 favors big forwards who can head the ball in for a goal, so pay attention
Choosing your Kick-Taker
Before you begin the game, I would recommend picking your kick taker in team management so you don't have to set it to your preferred kick taker every time you get a corner. Now, as to who you should choose to take your corner kicks; I recommend a player with decent power and passing. Most of the time, the default kick taker is already set for you but look at the stats of each player to determine who would work best. Another thing to take into account is that you don't want to pick a big tall guy as your corner taker, even if he's great at taking them because he would be more of a threat in the box. The The Premier FIFA 13 Guide has a lot of information regarding choosing the best player to take your corner kicks, along with a LOT of other information. See my review here.
Also note that a quick way to select your kick taker on corners is to hold down RT on Xbox or R2 on Playstation, which will bring down a menu of kick takers without you having to go to the pause menu to choose your kick taker.
Taking the Corner
The two things to remember when taking a corner are obviously direction and power. In terms of direction, you want to aim just in front of your tallest, strongest players, or the ones that tower over their markers to some degree. You want to give it quite a bit of power. Try to get the power bar in the area where it's around the yellowish-orange area. See the image below that explains what I'm taking about.
Sometimes, you might want to try curling the corner kick. Only try this if your corner taker is right-footed and taking a right-sided corner, and vice versa so that your corner curls away from the keeper.
The Short Corner
A feature that returns again in FIFA 12 after debting in FIFA 09 is that a player is waiting to be called up to around where the corner is being taken so the corner taker can play a light pass to him. If you do this when your opponent is least expecting it, it can be very effective. A useful technique is to have this 2nd man run up, play it to him, and try to get as close as possible to the keeper's 6-yard box and pass in to someone to put it away. However, most of the time there will be defenders in your way and you might still have to either go for a low cross or something, or you could try to use a skill move to get around them. The inverted-rainbow move is very useful for this.
Defending the Corner
There really isn't much more you can do to defend the corner other than pressing the pass button to head the ball out of the box for a teammate to clear. Another thing you can try is to bring out your keeper to punch the ball away by holding Y on the Xbox and Triangle for Playstation, but I would only ever recommend this if the cross is quite near to the keeper because the opposing player might get his head on the ball before your keeper gets his fist to it.
Created Set Piece Corner
In FIFA 13, you have the ability to create your own set pieces to use in games, and this includes corner kicks. Get creative and surprise your opponent with a unique set play. You can do this via the Practice Arena.