Some family history, including what I know about my last name
It's pronounced (using the guidelines in the Merriam-Webster Pronunciation Guide) as "pO - 'lä - shek. This follows typical Polish pronunciation pretty closely, putting the most stress on the penultimate syllable, and is actually a pretty good match (as far as I can tell with my limited knowledge of the Polish language) for the original spelling of Polaszek.
According to Polish Surnames: Origins and Meanings by William F. Hoffman, Polaszek is related to Polak, the term for a Pole. The szek ending is a diminuitive.
My great-grandfather Jozef Polaszek brought the family from Kelpin, West Prussia to South Dakota by way of Hamburg, the Augusta Victoria, arriving in New York on 20 July, 1889. His wife, Anna (or possibly Joanna) Fritze, daughters Franziska and Anna, and son Johann accompanied him. They moved to Minnesota between 1902 and 1904, and the family's been in Minnesota since.
There's a lot of uncertainty, since while I believe the family were all Polish-speakers living in a German-administered section of Poland, what I'll find in the records will depend on who recorded the information. A German government official would use German spellings for things. A Polish parish priest might use Polish, German, or even Latin for the church records.