Obsidian files are just Markdown files. So, if you share a file in any way (e.g., a sync service like Dropbox, emailing, whatever), you can have someone else edit it.
There’s no features supporting multi-user live collaboration (like Google Docs) yet, however. So it’s up to you to figure out how to manage multiple people editing at once.
The best option for continuous collaboration is probably to sync an entire vault via a sync service, then have your collaborators also use Obsidian. Otherwise they won’t be able to create links or navigate Obsidian syntax.
However, if they’re just editing something that doesn’t rely on Obsidian features, just sending them the markdown file is probably best.