Journal paper submission practices to improve review quality and reduce delay

In my experience as both and author and an editor, the number one thing to reduce the review time of a paper is picking the right journal:

• A paper well-aligned for a community is likely to get reviewed more quickly than one that is dubiously aligned.
• Even amongst good journals, some operate much more quickly than others. For ones that show: "received, revised, accepted" dates in addition to publication, you can check this directly in their archives.

Beyond that, the next big barrier is finding reviewers and getting them to return reviews on time. Recommend a couple of people who would be fast and enthusiastic reviewers --- but also leave off some obvious choices. Editors will take some recommendations (and if they're good folks who return reviews quickly, that helps a lot). They will also typically want the majority of reviewers invited to not be your buddies that you recommended, so only recommend a few and leave off people they are likely to think of on their own.

Finally, papers that are easier and more pleasant to read get faster reviews as well. Pay close attention to the flow of your narrative and the ease of grasping key points from skimming through and looking at the figures. Good reviewers will read the whole thing, of course, but if you make it easy for them to organize their mental framework, it will go much better and faster and you'll be less likely to get misunderstandings.

I'd like to add one item to jakebeal's answer: Keep the paper concise, including only what really needs to be in there. Concise papers make life much easier for reviewers, handling editors and readers.

By concise, I mean make the paper as short as you can make it, but no shorter. Ask yourself if you really need that extra parametric plot or table.

Push other material to Appendices (often useful in math-heavy theory papers) or Supplementary Material (often useful to describe minutiae of experimental procedures), or even keep it off altogether.

Avoid wordiness; it makes reviewers -and handling editors- weary.