当 dāng is the simplified form of traditional 當. The traditional 當 is a pictophonetic compound: the 田 (tián, field) at the bottom carries the meaning, while 尚 (shàng) above supplies the sound. The early sense centered on matching or facing a thing of equal value, as one field set against another, which is why so many of the character's senses circle around the idea of correspondence: serving in a matching role, being at the matching moment, and treating one thing as the equal of another.

The mainland simplification 当 keeps a cursive trace of the upper 尚 element (reduced to the small 小-like top, written with the ⺌ "small" radical) over a 彐-shaped base, dropping the field entirely. The two forms are read identically; only the script differs.

当 is a polyphone, and the reading splits the senses cleanly:

1. dāng (level tone). To serve as, to act as a role: 当老师 dāng lǎoshī (be a teacher). To be right at a time or place: 当时 dāngshí (at that time), 当地 dāngdì (local). And to be obligated: 应当 yīngdāng (ought to).
2. dàng (falling tone). Fitting or proper: 适当 shìdàng (suitable), 恰当 qiàdàng (apt). To regard or treat as: 当作 dàngzuò (treat as). And to pawn: 当铺 dàngpù (pawnshop), from which comes 上当 shàngdàng (to be taken in).

The thread through both readings is the same: a fit between two things. When the fit is a role you take on or a moment you stand in, it is dāng; when it is the suitability of one thing or the equating of one thing with another, it is dàng.

From "to match" grows a sense of fittingness that shades into obligation. If an action fits the situation, then it is what one ought to do. This is the dāng behind 应当 yīngdāng (should, ought to), a close cousin of 应该 yīnggāi but a touch more formal, common in written and legal Chinese.

The same root of "what fits, what is proper" gives the everyday 当然 dāngrán, "of course." Literally "as it ought to be," 当然 marks something as so obviously right that it needs no argument. Spoken on its own it is an emphatic "Naturally!" or "Sure!"

Shift the tone from level dāng to falling dàng and the character turns from "the role I take" and "the moment I am in" to "the fit of a thing" and "the equating of one thing with another." 适当 shìdàng and 恰当 qiàdàng both mean fitting or apt. 当作 dàngzuò means to treat one thing as if it were another. And from the sense of giving a thing for its matching value comes the old word for pawning, 当铺 dàngpù (pawnshop), and the vivid 上当 shàngdàng, literally "to go up to the pawnshop counter," now meaning to be deceived or taken in.

The tone is the only audible signal. 当时 dāngshí (at that time) and 恰当 qiàdàng (apt) share the same glyph; the falling tone on the second tells you it is the "fitting / treat-as" sense, not the "moment / role" sense.

Hold one idea at the center of 当: a fit between two things. In the traditional 當 it is two fields set against each other, matched in value. Every sense radiates from that match. Take on a role that fits you and you 当老师, become a teacher. Stand at the moment that matches the event and you are 当时, "at that time." Do what fits the situation and it is 应当, what you ought to do. So obviously fitting that no one argues? 当然, of course.

Then let the tone fall to dàng and the fit becomes about things rather than roles: a measure that suits (适当), one thing reckoned as another (当作), or value handed over at the pawnshop counter (上当). Hear level dāng and think role or moment; hear falling dàng and think fit or trade. The tone is the switch between the two halves of the character.