Hiya (cool avatar BTW)
As no-one's replied, thought I'd shove in my two cents - you can always search on "spyder", "oil" or "lube" on the natty little site search engine and you should get plenty of pointers.
Don't have a Spyder myself, but once you are happy with taking your marker to bits, it's generally a good idea to inspect O-rings, seals and parts which do a lot of moving around (bolt and sear) for wear and tear. If you are using CO2, you may find some build-up or grit on seals and rings that take a lot of punishment, so give those a clean. Get yourself a spares kit with replacements for O-rings, seals, springs, and even a spare bolt might not go amiss if your gun has seen a lot of action.
I don't play on a very regular basis, so I tend to keep my markers pretty heavily oiled at home, and then clean off the excess before I play. I hear KC trouble free, Gold Cup and Snake Oil are good, but check your manual first for recommendations. Often different parts of the gun require different treatments (e.g. a regulator usually requires a light grade oil as opposed to a more viscous one for a bolt). Petroleum based oils are generally best avoided.
If you just strip and clean your gun after each game, swap out anything that looks damaged or suspect, you will probably be doing all you need to keep your gun running fine.