or by implication

Students most often encounter the indirect allusion such as, for example, the typical Biblical allusion: "He said he washed his hands of the whole matter." This is an indirect allusion relating to Pontius Pilot who disagreed with the crucifixion of Jesus and publicly washed his hands to symbolize his detachment from and denunciation of the crucifixion to come.

Bulgakov uses both indirect and direct Biblical allusions starting from the first chapter. An early example of indirect Biblical allusion is:

His gaze halted on the upper storeys, whose panes threw back a blinding, fragmented reflection of the sun which was setting on Mikhail Alexandrovich for ever;

The Biblical allusion centers on the word "sun" and is augmented by the preceding words "blinding ... reflection." The conversation between Berlioz and Bezdomny is about Jesus Christ, and, in the New Testament of the Christian Bible, Jesus is identified as the Son of God: “Thou art my beloved Son; in thee I am well pleased” (Luke 3;22). He is also associated with blinding light through the transfiguration recorded in the Gospels:

he was transfigured before them; and his face did shine as the sun, and his garments became white as the light (Matthew 17:2).

As a result, anyone familiar with these portions of the New Testament would recognize this indirect allusion to Jesus Christ, especially since Jesus is the topic of conversation. Incidentally, the same quote also alludes to the end of Mikhail Alexandrovich's life through the idiomatic cliche phrase "the sun which was setting ... forever."

When a direct allusion is highly detailed and explicit, it is termed a reference, however, an example of a direct allusion is:

instead of the nativity or the arrival of the Magi you should have described the absurd rumours about their arrival. But according to your story the nativity really took place!

Here, Berlioz makes direct allusion to the recounting of the nativity, or birth, of Jesus and mentions the Magi who were visitors after the birth. The rest of Bulgakov’s story has further examples of Biblical allusions of both types. If one is acquainted with the Biblical source, then these will be fairly easy to spot. The strength of allusions--the ability to enhance the author's message or imagery--is also the weakness of allusions: The reader must know the source or the allusion is lost upon that particular reader and instead of clarity, the allusion produces confusion or obscurity.

Allegory teaches a moral lesson using symbolic figures or actions. It can be taught through art or literature. This novel is full of symbolism, so you could connect it to allegory in this manner. It is through the symbols that the themes of a piece of literature are shown, so in this novel, it's necessary to understand the symbolism to understand what the novelist is saying to us.

Some of the main symbols in the novel involve the sun and moon. Wolan, or Satan, is introduced as the sun sets. The sun is extremely hot and insufferable as Yeshua, Jesus Christ, hangs on the cross. The moonlight makes the Master feel irrational and insane. Simply put, the sun symbolizes sanity, and the moon represents insanity. The novelist uses the sun and moon to show us how Wolan's actions affect the other characters and how evil his actions are. 

Thunderstorms are another example of the symbols used in the novel, such as when Yeshua is on the cross. A terrible thunderstorm occurs when Yeshua dies, and the same kind of storm occurs again in Moscow at the end of the novel. The storms represent people, both past and present, who have suffered at the hands of cruel dictators and repressive governments.

Basically, the other symbols deal with the repression of the Soviet government. Anyone and anything that did not align with Soviet goals were banished or killed. The sins of the Soviet bureaucracy are represented by objects, such as the wine spilled by Pilate that won't wash off. 

This is all very general, so if you have more specific questions, please don't hesitate to ask.