There are too many rules to learn in 60 seconds, but there are basic standards that make for better writing and a better encyclopedia:
Use double quotation marks to quote something verbatim
On Wikipedia, "logical quotations" rule. That means punctuation is placed outside the quotation marks, unless the punctuation is used in the quoted material.
Ellipses are three unspaced dots that replace material omitted from direct quotations.
Use semicolons to make one sentence out of related material. These can also be used to separate items in lists to avoid confusion, which can happen with commas.
Use hyphens for hyphenated names, to link prefixes (non-negotiable), and create compound modifiers (the oft-quoted author).
Since commas are the most-used punctuation, they get their own lesson next week.