After you have the line dry & clean, then give it a good coating with a line dressing. There are many of these available on the market & I think they all work pretty well. Just follow any directions the product has.
Keeping your fly line clean & in good repair is a way to save you money in the long run. Think of all the fly lines you've owned over the years. Now, imagine how much money you might have saved if every line you've ever had would have lasted another season. I know that this is something that is often taked for granted, but keeping your line clean will help you fish better.