The following are some basic maintenance procedures that I perform on my spinning reels. How often you break down your reels will depend on how often you use them and how much abuse they take with each outing as well as how finicky you are about performance. Keep in mind that this is not meant to be an authoritative manual on reel maintenance. While spinning reels operate on the same basic principles, each manufacturer/model may be different than what is found on my particular Daiwas.
One: Layout
It's important to have a clean and well-lit work area. The ideal would be a dedicated work bench but having none, I use my kitchen island. The white tile gives a nice contrast to those little tiny parts found on fishing reels. Also avoid working on carpeted areas for the same obvious reasons.
Two: What you NeedI lay out all of the things that I am likely going to need BEFORE I get started. These include but are not limited to:
1) set of screwdrivers (both slot and philips heads)
2) pliers
3) knife
4) Corrosion X (metal protectant/light lubricant)
5) grease (Cals for gears/drags and Daiwa Blue for medium lube)
6) reel oil (Rocket Fuel for bearings)
7) white gas/Coleman Fuel (degreasing and cleaning)

toothbrush and Q-Tips (cleaning)
9) clean rag
10) small plastic container with lid
11) reel schematic diagram
12) small ziploc bags
Three: Cleaning the Drags
Most spinning reels have drags located in the center of their spool. The drag elements are accessed by unscrewing the spool knob off completely. The drag washers are usually held in place with a type spring clip (hexagonal). You can remove the clip using a fingernail. If you decide to use a screwdriver, take care that the spring doesn't go flying!
Four: Cleaning the Line Roller
One of the most critical elements of a spinning reel is the line roller. Due to its external location out there on the rotor, it can get gummed up pretty easily. A dirty roller can cause line twist and a rough retrieve. An inoperative roller can cause line fray and breakage. Fortunately, it's pretty easy to clean. Just remove the screw that holds the roller between the bail and the bail spring mechanism. The screw also acts as the roller axle. The parts of the roller on a Daiwa Capricorn are (from left to right): tiny metal washer, line roller, liner roller bearing and another tiny metal washer.