I actually took the time to study the actual source, out of sheer curiosity, and the idea behind it is quite simple. The most recent version at the time of writing this post is 3.2.1.
There is a buffer storing pre-allocated events that will hold the data for consumers to read.
The buffer is backed by an array of flags (integer array) of its length that describes the availability of the buffer slots (see further for details). The array is accessed like a java#AtomicIntegerArray, so for the purpose of this explenation you may as well assume it to be one.
There can be any number of producers. When the producer wants to write to the buffer, an long number is generated (as in calling AtomicLong#getAndIncrement, the Disruptor actually uses its own implementation, but it works in the same manner). Let's call this generated long a producerCallId. In a similar manner, a consumerCallId is generated when a consumer ENDS reading a slot from a buffer. The most recent consumerCallId is accessed.
(If there are many consumers, the call with the lowest id is choosen.)
These ids are then compared, and if the difference between the two is lesser that the buffer side, the producer is allowed to write.
(If the producerCallId is greater than the recent consumerCallId + bufferSize, it means that the buffer is full, and the producer is forced to bus-wait until a spot becomes available.)
The producer is then assigned the slot in the buffer based on his callId (which is prducerCallId modulo bufferSize, but since the bufferSize is always a power of 2 (limit enforced on buffer creation), the actuall operation used is producerCallId & (bufferSize - 1)). It is then free to modify the event in that slot.
(The actual algorithm is a bit more complicated, involving caching recent consumerId in a separate atomic reference, for optimisation purposes.)
When the event was modified, the change is "published". When publishing the respective slot in the flag array is filled with the updated flag. The flag value is the number of the loop (producerCallId divided by bufferSize (again since bufferSize is power of 2, the actual operation is a right shift).
In a similar manner there can be any number of consumers. Each time a consumer wants to access the buffer, a consumerCallId is generated (depending on how the consumers were added to the disruptor the atomic used in id generation may be shared or separate for each of them). This consumerCallId is then compared to the most recent producentCallId, and if it is lesser of the two, the reader is allowed to progress.
(Similarly if the producerCallId is even to the consumerCallId, it means that the buffer is empety and the consumer is forced to wait. The manner of waiting is defined by a WaitStrategy during disruptor creation.)
For individual consumers (the ones with their own id generator), the next thing checked is the ability to batch consume. The slots in the buffer are examined in order from the one respective to the consumerCallId (the index is determined in the same manner as for producers), to the one respective to the recent producerCallId.
They are examined in a loop by comparing the flag value written in the flag array, against a flag value generated for the consumerCallId. If the flags match it means that the producers filling the slots has commited their changes. If not, the loop is broken, and the highest commited changeId is returned. The slots from ConsumerCallId to received in changeId can be consumed in batch.
If a group of consumers read together (the ones with shared id generator), each one only takes a single callId, and only the slot for that single callId is checked and returned.