In almost all cases, if you wrote the node, you should be able to edit it. Simply go to that node, and edit it! For most node types, including notes (replies), there will be an edit box at the bottom of the page, where you can edit the text directly. For certain other types of nodes, you will have to click on an "Edit this node" type of link to get to a page with an edit box. Note that you need to be logged in to edit your post. This automatically precludes editing nodes written by Anonymous Monk.
As for deleting a node, this is an extreme measure that is appropriately not easy to do. You can't simply click a 'Delete' button. If you know of any node that you think should be wiped from the site, the canonical procedure is to consider the node for reaping. However, the ability to consider is available only to Friars and above. If you're below that level, you can discuss your wish in the chatterbox and get someone who is a Friar to submit the consideration for you.
PerlMonks is a place to learn. As often happens in real life, Perl Monks learn (and often learn best) from mistakes that they and others have made. If you make a mistake in a node and then delete it, you may be saving your pride but you are also depriving your fellow Monks of the chance to learn from the mistake. Only actual duplicates, spam, and obvious trolling should be deleted.
If you can edit the node, use <strike> tags to mark through your mistakes
and then add in your corrections as well as an explanation.
Many Perl Monks choose to leave the original text intact, and simply add an appendix
at the bottom of the post. In this case, insert an Update: header before the
new text. Here is an example of this style.
If you cannot edit the node, try posting a reply to it, stating your corrections. Or you can contact the janitors, as stated above.
Consider this scenario. You post a node that has a factual error in it, and then someone else posts a reply pointing out the error. If you then simply fix your original node, you also render the reply node meaningless, or at least confusing, because now this reply is seemingly referring to something that is just not there. The time the other person put into his/her reply to you is now wasted. In fact, depending on the situation, the reply's author may feel compelled to update his/her reply lest it appear nonsensical or downright incorrect, which is an unfair imposition on him/her.
This means that replies to your node limit how you can edit your node without impairing the meaning of the replies. If there are replies to a node of yours, make sure that your edits are done in such a way that someone reading the node and the replies will be able to understand why the replies were posted. This can be done by using <strike></strike> tags around deletions and/or by including an explanatory Update paragraph, as described above.
(Of course, there is a race condition here; if it is clear that replies to a node of yours are referring to an earlier version of it, the right thing to do is to add one more update to your node clarifying any potential confusion. E.g. "the reply by paco, referring to a typo in the original version of this post, was posted while I was fixing this typo. Sorry for the confusion.")
Conversely, if you want to protect yourself from having a reply of yours made meaningless by an update in the replied-to node, you can quote in your reply the text that you are referring to. Also, you can make an update to your reply, in response to the other update, if/as appropriate.
See related discussion: why a nodelet can be kept agains author wish?