First, the most obvious: epics are in verse. Many (like Beowulf) are in dactylic hexameter.The Inferno is rendered in the terza rima. This means:
Five accented syllables to the line (lines usu. consist of 10 or 11 syllables)
Three-line stanzas called tercets
Rhyme scheme aba bcb cdc ded (very noticeable--go look for it, you'll see)
Another epic convention is the use of similes (epic similes are actually a specific type of simile. Webster defines it as "an extended simile that is used typically in epic poetry to intensify the heroic stature of the subject"). Dante uses epic similes as well as the standard kind:
"Their eyes seemed like rings from which the gems had been dropped." (Similes Dictionary)
On this page are a few examples of epic similes.
Third is allegory. Epic poets use it to make a dual point in their writing. Examples don't just abound in this poem, the entire thing is an allegory. Dorothy Sayers goes to the trouble of pointing out the literal and allegorical images in the notes at the end of every canto. I'm not going to copy down a whole bunch of them, just bear in mind as you're reading that Dante intended much of this as a commentary on the corruption of the Church and the sinful nature of Man.
Cataloging. Ah, sweet cataloging. Anyone who has read The Odyssey or The Iliad has experience with cataloging. Dante catalogs virtuous pagans in Canto IV, tyrants in Canto XII, demons in Canto XXI, and reptiles in Canto XXIV.
My study guide of epic conventions (courtesy a teacher) lists Descents to Hell as one. Need I say more?
It also lists journeys.
The use of summaries within the work to have a "flashback" effect: each sinner who tells his own story fulfills the role of recapitulator.
Prophesies are also an epic convention. The shades in Hell have no knowledge of the present, but they remember the past and can dimly see the future. A number of them predict events (battles, deaths, Dante's exile) during their conversations with Dante.
The opening in medias res (in the midst of the action) is a classic epic convention seldom ignored by epic poets. In Dante's case we do not see the events that led to him waking up in a dark forest.
Epics often focus on the past as being more heroic and virtuous than the present. Dante supports this in his poem: Florentines are shocked to hear how the city has degraded, Pope Nicholas III mentions that as bad as he was Pope Clement V will be worse ("...to serve ye with uglier acts, a lawless Shepherd indeed" XIX. 83-83)
Ecphrasis. No, don't say "bless you." An ecphrasis is an extended description of the detail of an object. Most of the geographic features in Hell get this treatment.
Finally, last one. The use of epithets to refer to gods/goddesses, heroes, etc. In The Inferno some of the people who are referred to by epithets are:
Mary*
Beatrice
God*
Jesus*
Virgil
Some of the sinners are referred to in this manner as well.
*never mentioned by name in Hell (this is symbolic)