To edit other people's pages, you must have Owner or Editor access to the wiki. If you have Reader access only, ask the wiki owner or a member with Owner access to give you Editor access.
Access to a community wiki is managed in the community. Membership roles in the community are replicated in the wiki. Community owners can edit wiki settings, and Community members can create and edit pages in the wiki. Users who are not members of the community can read the wiki content but they cannot edit it. For more information, see the Communities wiki help.