Things to do before submitting a manuscript
Putting together also some advice from the previous answers, here is my suggested checklist:


Run a spellchecker :)
Prepare a cover letter. If the manuscript has a previous history (e.g., it is a modification of a rejected papers; overlaps partially with a conference proceeding), you should state it. Some may want to suggest possible referees in the cover letter; I find it ethically dubious, so I never do it. In case, you may want to suggest referees to avoid. (maybe we should have a separate question on this point). 
submit a preprint, either at your institute or on arXiv, or at least think about it. Check the terms of the journal you are submitting to (this is a great resource) to make sure you can; often the submission is the best moment to do it, since the journal can have no reasonable copyright claim on what happened before it.
Even if you don't submit a preprint, make a backup copy of the .tex and .pdf files. If you use source control, tag the latest version as "submitted". This way it will be easier to recover that exact version when the referee report mentions "line 4 on page 2".
Send a copy to your co-authors, for backup and self-archiving.
Relax and celebrate.


You speak about applying the journal style in the manuscript; I suggest not to do it at this point. Referees won't care; it is really needed only after the manuscript is accepted, or if an over-zealous editor asks you to do it. You might spend lots of time without reason, resizing figures and line-breaking formulas that will be dropped after the referee comments.