I will be relocating to Shanghai by March 1 of 2006, How far in advance should I look and find an apartment?

You will probably want to stay in a hotel for at least a week upon arrival and look for an apartment when here. Too many variables that can't be communicated via email.

Can begin looking at areas/prices/compounds at any time. Rentals seem to either get taken up quickly or sit for months. Better to allow for the time when here to see the actual premises.

Does your company offer as part of the package an int'l movers' group? They should take care of all the real estate options -- just be prepared where you're willing to relocate (e.g. Puxi or Pudong?). You would ideally need to do a "go-see" about 1 month before you relocate so you can check out the apartments.

So, if I want to move in March 1, 1-2 weeks before would be sufficient to find an apt and sign a lease? This being said, I will have several business trips there before and plenty of time to look at places to live.

It doesn't make sens to start looking too early as the good apartments move quite fast. Once you have decided in which area you want to live the choices for expats are normally limited to the newer high-rise apartments. And then it's just a matter of having a look for a week or 2 and you should be done.