In order to earn the Tag Editor badge it is written that one has to edit tag wikis. Can anyone suggest how to do so?
Every tag has an info page that you can get to by clicking on the tag name. Such as this one: calculus. You will be taken to a page that looks like this
(If the tag doesn't have information the page displayed will be slightly different.) Simply clicking on "improve tag info" will bring up the editor and allow you to suggest an edit to the tag excerpt (a short text consisting of tag usage guidance) and the tag wiki (a longer text which can contain more information about the tag).
(The "info" tab of this page will display both the excerpt and the wiki, and you can get to the tag info editor from that tab as well.)
I stress that these are just suggested edits, and users with at least 5000 reputation will need to approve them, so please only make worthwhile edits that decidedly improve these wikis.
Note, too, that just editing tag wikis in order to earn badges is not really good behaviour. A single wiki edit isn't going to matter too much, but spamming 50 tag wiki edits simply to (attempt to) earn the Research Assistant badge is a different matter.