how does asynchronous transfer mode works?

Answer 1

From Wikipedia

Asynchronous transmission uses start and stop bits to signify the beginning and end of a transmission. This means that an 8 bit ASCII character would actually be transmitted using 10 bits e.g.: A "0100 0001" would become "1 0100 0001 0". The extra one (or zero depending on parity bit) at the start and end of the transmission tells the receiver first that a character is coming and secondly that the character has ended. This method of transmission is used when data is sent intermittently as opposed to in a solid stream. In the previous example the start and stop bits are in bold. The start and stop bits must be of opposite polarity. This allows the receiver to recognize when the second packet of information is being sent.

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Actually you don't need start and stop bits, any handshake protocol between the transmitter and the receiver can be used.

Answer 2

The previous answer is somewhat flawed. His Wikipedia quote is for any general asynchronous communication system. Your question is specifically about ATM, which is used as a specific protocol used in fiber optic/ high speed copper communications systems typically on the backbone of the SONET standard used in data transmission for the internet and telephone systems.

ATM uses a fixed data payload system designed to compensate for asynchronous delays in clocking.
It's a fairly complex area to study, and assumes that the user has knowledge of the various communication protocols that led up to the standard. There were a number of ATM boards that were sold (for copper interconnect) that plugged into PCs in the mid '90s. Here are some links to the information.