Any tips as to how to move the ball downfield (up the pitch? Whatever the term is in soccer)? I can never seem to get into their territory and get a clean shot on goal.
Dont force it. Thats probably the most important lesson to learn.
If a simple pass isnt on, then dont feel bad about playing it backwards or to a player in space.
Its hard to give you exact advice without seeing you play or by showing you how I play but just try to follow these principles:
Keep it on the ground. (no point spraying it through the air, only Stoke do that, and you aint Stoke!)
Understand what your players are good at. (dont try to out pace Sergio Ramos with Fabregas)
Play to your teams strengths (pacey strikers and wingers or Andy Carrol target man)
The game is about possession, not about moving down field. (the ball can go backwards if it means you stay in control)
Use the counter attack when you can.
Learn the advanced pass/control buttons and when to use. R2 + x controlled pass, L1 + x one two, L1 + triangle lofted through ball.
Also learn to post up when defending. Defending is something which it takes a while to learn. No point in diving in or going to ground. Best way to defend is to wait until a player tries to go past you, hold off, post up, use the x button to get yourself close and force them into negative space, ie away from a good pass option. Let them make the mistakes.
I also scored a 28 yarder with Delph (wat) that wasn't saved in that 5-0 game. 
