Check for copyright violations. Long segments of text without wikilinks or citations can indicate that the text was illegally copied into Wikipedia. Look for other red flags. Instructions for reporting violations are at Wikipedia:Copyright problems.
Add wikilinks. Where appropriate, make links to other articles by putting "[[" and "]]" on either side of relevant words (see WP:LINK for more information) and check that your links work as expected. Note that dates should not be linked purely for the purpose of autoformatting; in general, consensus is that there are very limited instances where linking of dates is desirable. Please do not link terms that most readers are familiar with, including common occupations (e.g., "writer"), well-known geographical terms (e.g., "United States"), or everyday items (e.g., "milk").
Format the lead. Create or improve the lead paragraph. It should "define the topic, establish context, explain why the subject is interesting or notable, and summarize the most important points".
Arrange layout. Arrange section headings as described at Wikipedia:Guide to layout. Be sure that any stub template appears after any category links, separated by two blank lines.
Replace HTML tags with wiki markup, where available. Use of HTML tags is discouraged where equivalent wiki markup exists: for example, replace <b>bold text</b> with '''bold text'''. However, HTML is permitted where no corresponding wiki markup exists: e.g., H<sub>2</sub>O for subscripts and for a non-breaking space, though in pretty much all cases a template alternative exists (like {{sub}}) which might be preferred. Help:HTML in wikitext has a list of obsolete HTML tags and wiki equivalents for most tags; Help:Wikitext has even more wikitext syntax examples.
Add an infobox if appropriate. Add an infobox if it is appropriate for the article; use subtemplates as applicable.
For an article about a person, use {{L}} to add a sort key and categories. The three parameters of this template will automatically add a sort key, birth and death categories, and Category:Living people if true. For other articles, use {{DEFAULTSORT:}} to add a sortkey.
Add {{coord missing}} if missing. Does an article about a place or building not have the coordinates? Add this template, with a suitable region parameter. Better still, find the coordinates and add them, using {{Coord}}!