You normally don't need anything on a modern floating line except to clean it. If you use it a lot, probably at mid season and end of season; if not, then only at the end of the season. You canuse Armorall or use a cleaner made by the line manufacturer. I know that Cortland usually include a couple of felt discs with the cleaner in it with new lines; other manufacturers may not. You can pick some up at a fly shop. You can use Mucilin, but this is more of a line/leader dressing, but it will clean the line. Dirt on the line affects the shooting quality of the line, and can increase wear on the wire guides. I've personally never fished enough to ever wear out a wire guide, but I can hope. I've bent or crushed a few falling on the rod against a rock, but that's another story.
Just string it between two fixed points in your backyard and leave it hanging, then rub the line with a rag or felt pad with cleaner on it from one end to the other. Change to a clean spot on the pad or cloth and rub back in the other direction. Cleaned and dressed and ready to put away.
You can grease the leader with dry flies too. Use Mucilin or a fly floatant. This increases the surface tension on the leader and makes it harder to sink. Most of the time this isn't an issue. If you feel you need to do this, about 12-18" at the fly end should do it.
On old lines, you may need to use line conditioner fairly often. The line develops small cracks in the surface which allows water inside, wetting the core and changing the line density so it swon't float very well. A grease type cleaner/conditioner like Mucilin will fill these cracks and repel water, but will wear off after a couple of uses. When you notice some of the line under water, it's time for another treatment.
Scientific Angler also makes a great product for cleaning and treating lines. You can get it as a kit with a special cleaning pad and a bottle of the dressing. It makes the line significantly slicker and protects it from contaminents. It lasts much longer than Armeral. Keep your line treated a couple of times a year and you'll get an extra year or two of use out of it.
there used to be a powder you could use to treat floating lines - a line conditioner i believe that was supposed to be used 2-3 times per season. i haven't seen it for a while, maybe because of the newer lines? it didn't work great but helped with old fly lines.