It depends on the age of the collection account - or, more specifically, the last time you paid on it. If you threw a payment at it two months ago, then paying it down more this month will help to increase your score. If, on the other hand, you haven't touched it in six years, then you'll want to leave it alone. Dont send them anything - just let it fall off your credit report.
Back to the original topic. If you have a number of collection accounts, you will find it difficult (read: impossible) to improve your score quickly. Everything else in your file could be perfect, however, those collection accounts will continue to drag your score down severely until they actually fall off your report (seven years from the date you pay them off).