Whenever we head to the ironing boards during my classes, I usually have to remind my newbies to press rather than iron. Because most of us iron our clothing (and hate it!), we attempt to do the same thing with fabric. We iron...because it's fast and we want to get it over with. But there is a difference! When we sew and quilt, it's best to press!
Pressing: this is when you take the iron, put it on the fabric, hold it there, lift, move to another area, place the iron down, hold it there, lift, move to the next area, and so on. You press one area at a time.
Why Press? The problem with ironing is that the pressure and movement distorts the fabric and makes the fabric wonky. How so? The threads that make up fabric are woven in straight lines; when you iron, you push those threads all out of whack. So when you cut it, it looks fine; when you sew it looks fine; but when you wash the item and the fabric straightens itself back out, it doesn't look so fine. Then you have weird bumps and such. My friend who quilts refers to those bumps in order of severity: A cups, B cups, C cups...I think you get the point.
If you really struggle with wrinkles, use starch. And to make it even easier, remember that the heat from the dryer bakes in wrinkles, so when you wash the item or fabric, take it out of the dryer when it is damp and hang it.