This sort of question pops up frequently.
The regular Infiltration skill is used for sneaking against astral observers.
Not astrally present:
PC's Infiltration + Agi (+/- modifiers) vs. Astral Observer's Assensing + Intuition (+/- modifiers)
PC rolls normally. Astral Observer may likely recieve bonuses to their roll due to astral contrast (an aura in an area that is mostly shadows or the reverse, etc), or from superior positioning.
Note: This type of observance is usually not looking for everything but instead particular things such as spell auras, astral forms, sudden background count generation, etc, unless the guarded area is highly valuable. Mostly because it's typically a waste of resources to use magical assets to do what drones can do and also to have spirits memorize hundreds of employees... well even a F6 with 100 memory rolls to make will get a few no hits, glitches, and crit glitches... depending on orders this can range from being just annoying to dead wageslaves.
Astral Perception or Dual Natured:
PC's Infiltration + Agi (+/- modifiers) vs. Astral Observer's Assensing + Intuition (+/- modifiers)
Basically the same as above. The PC is still in their meat body and must use physical stats for this action. This is also a physical action and many GM's would give them the -2 penalty for a physical activity while astrally perceiving. The only major difference here is that in this case the PC will be an astral FORM and not just have an Aura. If an Aura shines well against shadows like a candle, then a Form is like a halogen headlight.
My rule of thumb is to give an astral observer a +2 for Auras in a high shadow area, a +4 (basically a bought hit) for Forms in a high shadow area, +2 for Forms in a high aura area like a dense forest or jungle, etc.
Astral Projecting:
PC's Infiltration + Logic (+/- modifiers) vs. Astral Observer's Assensing + Intuition (+/- modifiers)
Page 192 of SR4A lists what mental attribute to use in place of physical ones when fully in the astral. Again, the PC will be a full astral Form, so use positive modifiers for the observer to reflect how much easier it is to notice them.
Astral and Sneaking has been discussed at length on DumpShock as well. I can come up with the links if anyone is interested.