When to use this writeup
You have a pair of trousers (not necessarily your own, although I'd have to ask what you were doing with someone else's trousers), clean, dry, and crumpled, made of some material like cotton, polyester, or linen, such that the care symbols indicate that it can be ironed in your own home without risk to life and limb. (Do not under any circumstances try this with jeans. Physicists have found that this disturbs the fabric of space-time, a hazard called the Jeans instability1.)
You have an iron and ironing board with the necessary supplies of electricity and water. In a hard water area, tap water is not recommended. Better use low-mineral content bottled water, or for the ultimate in ironing convenience distilled water or de-ionized water.
You wish to impart to said trousers not only a lack of unsightly crumples and creases, but also the straight, razor-sharp back and front creases that will prove to the world that you are a man of taste and judgement, or at least possess enough gumption not to screw up the task at hand. (If you are a woman, then your trousers are a different shape and I will not be able to satisfy you on this point.) (If you are a man totally lacking taste and judgement, what are you doing on this website?)
However, you are, rightly, wary of the power of the steam iron to create near-indelible creases. Although you are able to achieve the blank page of the perfectly smooth garment (with the iron set for preference to medium hot, maximum steam), the pristine surface confronts you as the virginal sheet of foolscap does the writer, or the blank canvas the artist.
If your first stroke is misplaced, you will either have to continue along the same lines, creating a symmetrical but absurd configuration bearing no sensible relation to the legs of the intended occupant, or to superimpose your corrections on the first crease -- creating a double crease that shows that you have, to put it plainly, screwed up.
Why the method works
Luckily, this is the point where the men's clothing industry comes to the rescue. The basic design of trousers is a thing well known and extensively researched: with a few variants (front pleats or no pleats, cuffs or no cuffs) all trousers are constructed the same way and have been for decades. The exact cutting of the pieces and positioning of seams has been fine-tuned to the point where almost any set of male backside and legs, no matter how strangely shaped, can be given a civilized appearance.
One major factor in the precision design of trousers is the tendency of men to leave their hands in their pockets. This presents a problem relative to the front creases: the hands might interfere and create strange creases and bulges of their own. Not an attractive prospect. The problem is brilliantly solved by making the ends of the pockets coincide with the front creases. No matter how enthusiastically hands are jammed into the pocket, they will only reinforce the crease.
How to do it
Working one leg at a time, lay the trousers along the ironing board, the waist and the other leg hanging off the pointed end of the board. The outside seam should be facing up at you roughly in the middle of the leg.
First determine the bottom end of the creases. You usually can't go wrong by putting the outside seam on top of the inside seam and then ironing the bottom inch or so of crease at front and back. If there are cuffs, you have to iron the fabric both outside and inside the cuff. If your feet face outwards, you might want to make the front crease end a little nearer the outside seam -- putting the outside seam an inch or so forward of the inside seam.
Now to the top end. Insert one hand into the pocket and find its bottom corner with your index finger. Wiggle it around a bit to find the stable equilibrium point. With your other hand, find the corresponding point on the exterior surface. This will be the top of the front crease.
Now, keeping hold of this point, gently smooth the fabric back on both sides of the leg: you will then find the top of the back crease.
Now the task appears simple: to connect top and bottom with a straight line. But if you pull the front crease straight, it will tend to bend the rest of the leg out of true, and vice versa. What to do? To circumvent this apparent non-Euclidean geometry, pull the outside seam into a straight line. The front and back of the leg can get out of shape through wear, but the seam is the strong backbone: if the seam is straight the rest will follow.
Then you can run the iron down from the top to the bottom along the outside seam, and finally along the front and back creases, having checked that they are properly aligned at both ends and that there are no crinkles on the underside. If there are pleats, the front crease should come up to meet them, but no further. If not, it can go up to the waist. The back crease can come up to within a few inches of the waist. (The back creases should not meet in the centre. That would look weird.)
Once the creases have been made, you can turn the leg over and have at them from the other side, until the required degree of sharpness is achieved.
The Art of Pleats
Now, what about those pleats? You should find either a single pleat more or less aligned with the front crease or a double pleat with the inner pleat so aligned. You should now be using the pointed end of the board by putting it inside the waist, allowing you to work on the front of the trousers. Pleats should not be sharply creased. You don't want your sub-waist area looking as if an origami master has been at work on it. So you have to use the iron gently to smooth the bits between the pleats without actually squashing the things flat. The ideal result is a set of rounded, downward-pointing undulations like an expensive set of curtains. The inner pleat should segue into the front crease somehow.
To fold the trousers, take hold of the front belt loops and bring them to the front. The portion of fabric between them folds inwards. Thus, you can lay the garment flat while respecting the creases. For storage on a coat hanger, usually one folds again at the knees. However this can impart a conspicuous horizontal crease . Better is to put the bottom of one leg over the bar, then the bottom of the other leg over from the opposite side. Like this:
This is equally stable and for some reason leaves the legs in better shape.
Finally, enjoy your trousers and don't forget to use napkins while eating!
1. Yes, this is a real term in astrophysics.