Tap on any place on the map, then tap the star symbol ("Save" button) in the left down corner of the place page to add the place to bookmarks.
Note: for open areas you will need to tap and hold the map for a second to see the place page.
To delete one bookmark, tap the bookmark on the map, then tap the star symbol ("Delete" button) in the left down corner of the place page.
To delete a list with bookmarks (all bookmarks in the list) tap the double star symbol on the main panel → tap the icon with three dots in front of name of a list with bookmarks → tap "Delete" in the pop-up window or tap the list with bookmarks to delete them by one.
Note: the "Delete" button is active only if you have more than one list with bookmarks.