A disguise is more than changing the appearance of your facial features, or quickly swapping your clothes. While these do enter into the greater spectrum of disguise, a person can retain their basic overall appearance, but still be completely unidentifiable as who they really are. The application of an accent and a diversion from their normal behavior and demeanor can misdirect pursuit quite effectively. Add to this a few inches more or less height, a dozen or more fewer or extra pounds, ten years more age, and a few missing, or suddenly acquired, teeth, and only a dog will recognize you. Apply or remove something to alter the scent that the animal has attributed to you, and this problem disappears as well. But it is understandable that a less confident novice in this art will be disinclined to rely on such subtleties. They are the marks of the experienced "shape-shifter".
This term has connotations of some sort of metamorphing creature of myth or magic. But that is truly what disguise is. Most people's impression of a person's shape subconsciously includes the peripheral details of how they walk, how educated they sound, both in grammatical propriety and enunciation, how clean they are, which immediately produces an assumption of their lifestyle, and many other factors of the way they enhance, or detract, from their surroundings. So a person that looks just like "that wealthy fellow that just tuned that corner", will never be mistaken for "that bum coming back the other way", from that same corner, even though he may be wearing the exact same clothes.
Why? Because he took a few moments to untie a shoelace, rumple his hair and jacket, and smear some foul-smelling sludge in his pants. The addition of a limp, or the muttering of some delusional nonsense, will add to this failure to identify him for who he is. In fact, the searcher will most likely make a face and go to some effort to increase space between himself and this "undesirable". A good deal of what makes a disguise efficient is the time spent considering the environment this disguise will be employed within. Poor people tend to know what a legitimately poor person looks and acts like. Likewise the rich. They know their own, but are less familiar with the true earmarks of the "other half".
What must be remembered is that a disguise is not always the addition of appearance changing elements. In many cases, the best approach is to begin with numerous alterations, and effect your disguise by shedding them. Here again is that necessity of considering where you will be when you need your disguise. if you're going to be in an area where people know you, then the former approach is probably best. If not, the latter is preferable.
But given that significant appearance changing items are desired, they are not difficult to obtain, or even create yourself. Padding from any old chair can be used to add the appearance of weight. A handful of straw stuck under a cap can give the impression of an unruly mop of blonde hair. A simple slouch goes a long way to alter an appearance. A few layers of shirts work as well as reversible clothes for quick changes. Flour can add gray to your hair, assuming it's not raining. There are sources of coloring that can be applied to your skin to give the appearance of a sunburn or an entire change of race.
Top grade paraphernalia probably needs a "connection" with some member of a city's criminal element to be obtained. A Theater group can provide similar items, if you can get hold of them. These are such things as bald wigs, false beards, reversible jackets, face putty and paint, adjustable-sole shoes, eye color lenses, false teeth and other disguise classics.
It has always been appreciated by the shadier part of a city's population that entertainers are reluctant to discuss their trade craft. Because such items are not immediately considered when a posse turns a corner and does not see the man they were pursing. Only very experienced watchmen will stop and gauge how nearby folks would look if they were a little shorter, or a bit older, or blonde, or what have you. By that time, the target has turned another corner and altered his look again.
For this reason, a disguise often only needs to work for a bit or two. But then it must be discreetly discarded. Arrests have been made on innocent people just for the suspicious fact of them having such items on their person. Pity the bum that finds a "nice jacket" in the trash heap, and is then arrested for burglary.
This person has learned that better paraphernalia is available, and are making efforts to secure a source of such things. He may have been lucky enough to stumble across an incident where someone wearing some real disguise wear was found out, and had a chance to see what sort of tactics they employed. He is now trying to copy those tactics, but is also aware of the fact that the man whose tactics he is copying ultimately failed.
This man has found a connection to obtain some better items to wear. But he is learning the tactics enabling him to not rely exclusively on them. His confidence in his ability has improved to the point of bluffing his way past a curious guard with feigned indignation, his disguise lending credibility to his act. But he may still run into a guard whose confidence in his own skills undermine this confidence. Or worse yet, a relative of the man or woman he's pretending to be. In this case, he'd best also have a better-than-average skill at running.
Now we are going beyond mere disguise, and entering into the realm of actual "impersonation". This man is capable of improvising changes on the run. He uses the appearances of those around him to confuse the issue by copying them. He would be able to approach the pursuing guards with claims to have seen the man they're chasing, and be believed. Only an adversary who has also had specific training in disguises has much chance of seeing through this man's facade. From a distance, he can impersonate a specific person effectively, and would be cool enough to have prepared something to divert the attention of anyone approaching him at the time.
This is truly the "man of a thousand faces". His skills seem to go beyond mere enhancement, and border on actually altering his physical structure. It is almost impossible to tell what is his true appearance. Even those who know him can be fooled face to face. He is skilled enough to lean into a doorway for just a moment, and come back looking different. And the paraphernalia he uses to effect these changes are also disguised to seem innocent. A person would swear he had to make this change without the use of his hands, only to find that the arms themselves are fake. And when he needs something to disappear, it's as if it went up in smoke. No one really knows for sure how tall, or how heavy, or what race, or what eye color the man possesses. And on the rare occasion that something does go wrong, it seems as if it was part of his plan, because he has caches of disguise items already in place along his path of escape.