How do comic books tell a story?

Comic books tell stories through "sequential visual storytelling." For a thorough analysis of comic book storytelling, I highly recommend Scott McCloud's book Understanding Comics, first published in 1993. Links below.

For a simple example of sequential visual storytelling, imagine a sequence of three visuals: in the first visual (or panel), there is a banana peel on the sidewalk and a man is walking towards it. In the second panel, the man is stepping on the banana peel. In the third, the man is sitting on the sidewalk with a dazed look on his face. When these panels are read in order, they tell the story of someone walking down the street and slipping on a banana peel.

This is an example of a three panel comic strip. Comic books are a longer narrative form, consisting of sequential illustrations on multiple pages that are bound together into a book or booklet form.

Comic book pages are typically broken down into smaller panels which are meant to be read in sequence. The panel layout determines the order they should be read in. In American comic books, panels are typically supposed to be read from left to right and from top to bottom. If another panel sequence is intended, or if the sequence is unclear, sometimes small arrows or numbers will be added to indicate the correct sequence to "read" the panels in panels.

Note that "read" is in quotes. That's because Comics have a vocabulary and grammar in both the prose and the illustration, so it's necessary to "read" the images in a comic book even if they don't contain any text.

One can draw some comparisons between comic book visual vocabulary and film vocabulary, and in fact, a film storyboard bears some similarities to a comic book, using a variety establishing shots--"splash" shots, mid-shorts, over-the-shoulder shots, close-ups, and so forth--to create a rhythm of images and help propel the narrative along.

However, many comic books layouts break free from presenting a sequence of same-sized rectangular panels (as a storyboard would) and instead the artist strives to create an overall design for the entire page, using a variety of differently shaped and sized panels in a variety of positions, along with negative space. Will Eisner and Jack Kirby are two comic book storytellers/artists who helped innovate comic book layouts back in the 1930s and 1940s.

The size and shape of panels affect the pacing of a story. A sequence of similarly-sized panels with similar (or even identical) illustrations can be used to decompress or slow down a story, akin to a long take in film. A sequence of panels with very different illustrations can be used to compress or speed-up the action in a story: quickly jumping from scene to scene.

It's possible to tell a story entirely through visuals, with no text. The Owly books by Andy Runton do this. More typically though, text is employed. Narrative text from an unseen narrator will typically be placed in rectangular caption boxes. Character dialog is typically placed within speech balloons, with a pointer, called a tail, pointing towards the character who is speaking. If the character is not in the illustration, a speech balloon pointer might point to where they are standing outside the frame, or perhaps a caption box will be used, with quotation marks to clarify that it's dialog and not an unseen narrator. Just as the placement of panels indicate the order in which they should be read, the placement of dialog balloons within a panel indicate the order in which they should be read.

Character thoughts are indicated by thought balloons, which are similar to speech balloons but instead of a tail, they use a set of increasingly smaller circular bubbles leading towards the character who is thinking.