you need to create a sliver of space before you shoot the ball. otherwise you will just be pinging it off of defenders,
as for how you took 23 shots, and scored no goal I'm assuming at least half of them were not on target (ie the goalie, didn't even have to save it) So get shots with a chance of doing damage, not just shots for the sake of shooting
this goal was scored on legend difficulty, there are plenty of goals to score in fifa13 I love how realistic they come. see how I got in some space and set up my strong foot?
http://www.easports.com/media/play/video/143455798
Ill show another goal, just that this one was called offsides. I still dont know how
http://www.easports.com/media/play/video/145843882
Now dont go off and try to recreate myne or any kind of goals, just use my advice at the front. Get in a good, dangerous spot, find some space, take your best shot .