What parts should you lubricate an air rifle?

This is a little hard to answer because you didn't state what type of air gun you are trying to oil. Is it a C02, Pump, Springer, Nitro or PCP air gun. But let me give some general rules. First NEVER use regular oil, it will eventually eat the seals. Only use air gun oil like Crosman Pellgun oil, RWS oil or other pellet gun oils. Regular oil is not good for airguns.

Oil the moving parts but don't over oil them and make them sloppy. there are some Excellent videos on air gun care on the web I suggest to take a look. See the link below.