It takes 1500 reputation to vote to approve or reject an edit to a tag wiki — or 4000 reputation to apply one immediately — but anyone can suggest one just by clicking the Edit Tag Info button:
This will put your edit into the Suggested Edits Review Queue, where it can be reviewed and accepted (or rejected, as the case may be) by anybody who does have sufficient reputation to do so.
If you want to know if your suggestion is still pending, or if/when it was ultimately accepted or rejected (including the voting breakdown which would explain why), you can check in your profile under the Activity→All Actions→Suggestions tab:
If you've already made the suggestion and had it rejected — or if it seems to be taking an unusually long time to get processed — you can then bring it up on meta to get more focus on it: Explain as best you can what your suggested edit was and why it was an improvement on what was already there, and open the discussion to the community to decide how best to handle it; be willing to accept any input the community has to offer to further improve your own edit-attempt. Any future attempts to push the edit into the queue can then link to the relevant meta discussion in the revision comment.
Unless something is blatantly inappropriate (e.g. offensive language, spam) I see little need to report a problematic tag-wiki entry before all the above steps have been taken: If every reasonable attempt to apply the edit yourself and/or discuss the issue with the community has failed, then direct moderator intervention may be needed. In such cases, you can simply raise a flag "In need of moderator intervention" on the meta discussion itself with a detailed explanation of the problem.