Catbox excitement over a rarely-seen Unicode smiley face lead me to believe that there may be some interest in this topic.
Naskh script, (also spelled nashk, naskhh, or sometimes nashik) is a specific calligraphic style, or "font", used to write the phonetic alphabet used in Arabic, Pashto, Farsi, Dari, Urdu, and other languages around the world.
It was derived from the Thuluth script, and replaced Kufic, as a faster to write, easier to read, and generally more aesthetically pleasing script. Its successor for many purposes is Taliq, a more ornamental script, though naskh is still in wide use in much of the world. Your browser probably uses a naskh rendering, as do most printed materials.
This writeup focuses on the naskh script as used in the written form of the Pashto and to a lesser extent Dari languages, and may bear idiosyncrasies, letter forms, or even entire letters that are not applicable to other languages.
There are a few basic concepts in producing Naksh script that can be confusing at first to a first-time reader. One of which is easily explained: it is read from right to left.
The most problematic of these is probably the concept of place-dependent forms, which can be extremely confusing, as it uses a completely different set of visual cues than Anglicized writing systems. New readers of script tend to focus on the "riders" of a letter (which will be discussed later) rather than the entire segment occupied by a given character on a line of script. This confusion is further compounded by the fact that native readers (what few there are) often focus more on the importance of the riders when teaching, not understanding how alien morphing forms can be, especially given that there are more letter forms than there are riders.
A given letter, itself a representation of simple phoneme, can have three distinct base shapes, not counting those that may be used as diacritical marks, as و is seen in the word کړُت or specialized characters such as the "crown" seen only above the letter ل (lam) in the word اللّه (Allah).
The three major forms are denoted by their position in a particular word -initial, medial, and final . Some will refer to a fourth form, "isolated", but the isolated form of a letter is generally either its initial or final form, most commonly the latter.
Initial forms are those that come at the beginning of a word. For instance, the character ق or "qoff", when in the initial position, is written as قف, seen here in the Arabic word "Qeff".
Its medial form, or the form as written between two connecting letters, is نقل, as seen in the Pashto word "Nuqul".
Its final form is the same as its isolated form, as seen in the word تتبیق, "tutbiq".
There are several "families" of letters that share the same forms. ح , س , ب , ص , ی , د , و , ر , ق , ط , and ک are the base forms for most letters, with a few oddballs such as م , ا , ه , and ل that have special rules of their own. Derivative letters differ mainly in the number of dots, or "takei", that they have and in what position those takei are placed. Example; ح (hay) versus څ (tsay) or ج (jeem). Some letters use non-takei marks, such as ذ (dzay) which is a د (dal) ridden by a hamza.
The "family" of a letter determines not only its forms, but also how it may connect or be connected to the letters near it. For example, ا may not connect on the right side with any letter, except for ل, where it may form a special combined character, ﻼ , which unfortunately does not often render correctly in Unicode. I will depict it below with crude ASCII art:
The simple construction of a particular piece of script often does not necessarily allow one to read it properly, unless full diacritics are in place (which they almost never are). These diacritics (as have been previously illustrated in above examples) serve the purpose of identifying the "hidden vowels" between depicted characters.
For example, the word دسته can be read as either "dasta", a sheaf of papers/arrows/flowers (don't ask, it doesn't translate 100% to English), or "dasatah", the handle of a (any) farm tool. Without context, there is literally no way to tell, without diacritics.
In many dialects of Arabic, new letters are introduced on a haphazard and non-coordinated basis as an aid to "Arabization" of usually English words. For instance, in Qatar you will often find neon signs with a letter found nowhere else - a "toy" form with four takei riders. It is taken to mean a soft "th" sound, as in the English word "the", rather than using a "say" or "zoy".