I can’t tell you the perfect balance between description and dialogue when introducing your story, or anywhere in the story, because this varies from writer to writer. Some writers prefer dialogue heavy, others description, some are in the middle and others vary depending on what story they’re telling. When you’re writing though the question in not a matter of numbers, how many paragraphs of description or lines of dialogue, it’s a question of balancing situation and prose.
By balancing situation and prose what I mean is that if you open your story with an action scene you don’t want reams of deep description that slow down the narrative but at the same time you might not want lots of dialogue either. So, you may find yourself with a description heavy chapter but it’s short sharp sentences describing mostly action over surroundings. ‘He pulled out the chair and sat down’ is a quick moving sentence and implies quick movement. Whereas ‘he pulled out the old wooden chair and sat down at the rickety table’ is a slower moving sentence and implies slower movement.
When we talk about description it doesn’t simply mean description of setting or people but the description of action too. As such we need to consider what movement we need to describe as well. For instance we don’t always need to describe someone crossing a room or walking through a door unless it’s significant because the read can surmise that the character moved from one position to the next. This movement couldn’t also be shown by a short mention of the change in the scene; if we know they’re outside in the corridor and then there’s a mention of something they pass in the room we can gather the characters are in motion. Techniques like these can help streamline our beginnings and save unnecessary description that would slow the story down.
Similar rules apply to the dialogue, we don’t count the lines we count the necessity: Does the reader learn what they need in that chapter? The best way to do this is to cut extraneous dialogue such as greetings. I know I’ve mentioned this before but when we’re writing common courtesy goes out the window. Rarely in fiction do characters walk into scenes and greet everyone, unless the greeting is showing the reader something about how the characters react. There’s rarely small talk in fiction, all the dialogue tells us something about the characters or the situation. If characters start talking about the weather it tends to indicate awkwardness or segues into something else rather than being simple chit-chat.
These things are particularly important to remember in opening chapters because you’re trying to get your reader to carry on reading. Once readers are invested in characters and story they tend to be more inclined towards scenes devoted to character rather than plot. This isn’t to say you can’t make character scenes work at the beginning of a story but to do this you have to be aware that the beginning of a novel needs to draw the reader in, if it’s a character scene it needs to intrigue the reader and make them want to read on.
Whatever balance you choose for your work you have to remember that the beginning of your story is your first impression, the wrong beginning can put a reader off reading any further. Finding the right beginning is a balancing act between information and forward motion and, unfortunately, no-one can give you iron cast rules for how to do it.