By default, SMF allows each member to edit their own posts. Moderators are able to edit everyone's posts, including their own.
There are two methods of editing a post. Modify redirects the member to a posting page where the edits can be made. Modify message allows the member to edit the post inline, but the interface for Bulletin Board Code is unavailable. Bulletin Board Code would, therefore, need to be manually entered into the post.
Modify
To modify a post, select Modify. Make any necessary changes and then select Save.
Modify message
This can be performed by selecting located in bottom right hand corner of every post. This will open the post box. On selecting Save the changes are made instantly.