Pronounce your "th" like a "d" if it falls at the beginning of a word. Instead of saying "these" and "those" say "dees" and "does."
Say "bat" instead of "bath." If a "th" is at the end of a word, say it like a "t." If you say the word "beneath" with a Polish accent, you would pronounce it "bahneet."
Accent the wrong syllable. When adding an "ing" to the end of a word like "going," instead of putting the verbal accent on "go" put it on the "ing."
Omit an article before a noun if you're portraying a character that doesn't speak fluent English. Instead of saying, "That is a cake." Say, "Dat is cake."
Refer to people as a "that" and misuse the language in minor ways, if your character doesn't fully know English. "Dat is big girl" is an appropriate misuse of the language, when attempting to convey a Polish character new to the language.
Raise your voice, as if in question, at the end of a declarative sentence.
Accent the middle of the sentence when asking a question. "You go to da store?" You would have the accent on the "da" and the voice would drop at the end, instead of raise, as a question normally would.