If you’re accessing your own posts, you want to use the Micropub API. That is the main API for creating new posts, uploading photos, editing posts, and downloading a list of posts. If you’re building something just for yourself, you can generate an access token under Account → App tokens. That needs to go in an Authorization header when making requests.
As a quick overview, getting posts and paging through them looks something like:
GET https://micro.blog/micropub?q=source&offset=0&limit=50
Authorization: Bearer ABCDEFGH
For more about Micropub, see this help page: Posting API
Or this chapter of the Indie Microblogging book: Micropub · Indie Microblogging
Let us know if you have any questions!