How to iron ANYTHING. I was expected to know how without being taught and, no matter how hard I tried, I couldn't do it PERFECT ENOUGH! Nowadays, I look for clothes that don't need ironing or just stick to T-shirts and blue jeans.
Well, to start... you need an ironing board and iron, though in a pinch - any flat surface that you can lay towels on to absorb the heat and won't be damaged by heat or steam, will do. 2-3 towel thicknesses should give you enough cushion to avoid hard creases and protect your counter top or table (NOTE - see below; never set down a hot iron on an unprotected surface!). A spray bottle with water can substitute for a steam iron, too... and actually, with some fabrics, I prefer this to steam. You don't want to soak the fabric; just dampen.
I learned by starting with hankerchiefs - but a placemat or any other flat item will work. Spread the item out, hand smooth it as best you can. It's OK if part of the item drapes over the side... you'll change it's position as you iron. You want to iron only 1 thickness of fabric, when it comes to say, pillowcases or garments - otherwise you'll be ironing in creases on the other side of the garment. For instance, shirts - you'll want to lay one side of the front on the board at a time while you iron. With a pillowcase or skirt, slide one thickness over the pointy part of the board and then reposition, as needed.
Heat up the iron to the setting that's designed for your fabric. Too hot an iron will cause delicate fabric to immediately curl up into wrinkles that will never iron out (ruined) or even scorch in the pattern of the iron. Things like nylon, chiffon, some silks... require a very low setting. Cotton settings are hotter and I always use this most often. Some irons will have a wool setting, too. Linen is usually the hottest setting. At first - don't even mess with the steam option; if your iron is a steam iron, it most likely has a "dry iron" setting.
Use the spritz bottle to lightly dampen the fabric. With one hand, hold the item at one edge... with the other, lower the iron close to the opposite side of the fabric. Hold the iron however it's most comfortable for you - point toward the holding hand or the side of the iron. It doesn't matter, except for what will fit in the area you are ironing. You'll keep a light tension on the fabric with one hand and glide the iron over the fabric with the other, toward the hand that's holding... be careful of how close you get to the other hand. I still burn myself from time to time. Usually, the iron will be hot enough that simply gliding in a constant motion is all you need to do. Sometimes, you'll want to hold the iron in place - but never more than a few seconds, unless you have heavy fabric and really stubborn wrinkles.
IF you iron a wrinkle or crease into the fabric, use the spritz bottle again on the crease and let it relax the fabric before pressing it out again. Sometimes, if the crease is too "hard"... only rewashing will get it out. When you've ironed over the flat surface of the board, set the iron down and reposition the item if it is larger than the board. NOTE: when you set the iron down, set it vertically - set it up either on the board or face down on the new silicone iron mats, so you don't leave a burn mark.
Then, practice until it starts to feel natural. Move up through simple garments... then shirts with collars, sleeves & cuffs. You'll figure out what works best for you. I learned to iron shirts on the pointy end of the board, but in college someone did a how-to iron demo in public speaking, and she suggested ironing the more square back of shirts on the other end of the board. There isn't any one "right" way to do this... however you get satisfactory results is just fine!! I find that most of the process of ironing is just figuring out how to hold things, hand smoothing, and keeping enough tension on the fabric, so that the iron doesn't roll the fabric over into a crease. Everything else, is just practice and experience.
