In 2010, I worked part year in NJ, then part year in NY (changed jobs). I've lived in NJ for both. Do I need to submit an IT-203-B Schedule A along with the IT-203?

The concept of "allocation" is new to me with regards to taxes, so I'm kind of at a loss. Some of the language in the NY State forms seems to imply that allocation only applies to a single job (single employer) where you split time between one state and another, but then other statement I read make me think otherwise.

You do NOT need to allocate; it is done FOR you by the W-2s.

The instructions are indeed confusing, but the instructions for IT-203-B specifically says "complete a separate schedule A for each job for which your wage and salary income is subject to allocation." Since you had one job for which you worked solely in NY, and a 2nd job for which you worked solely in NJ, there is no need to allocate wages for either job. Therefore the data you put in the two columns of IT-203 (The Federal amount column and the NY State amounts) will exactly match what your two W2's say, and there is no need to file IT-203-B.