Władysław Miodunka is the author of some of the best materials for native English and French speakers who want to learn Polish. His series, "Cześć, jak się masz?" ("Hi, how are you?") includes the books "Spotykamy się w Polsce" ("We Meet in Poland") and "Spotkajmy się w Europie" ("Let's meet in Europe"). These colorfully illustrated books come with good audio materials and present grammatical information, both in charts and in the contexts of natural-sounding dialogue, which follow the story of the Nowak family and their French foreign exchange student, Michel, who takes on the role in the text of someone learning to speak Polish.
"Mastering Polish," a textbook by Albert Juszczak, is another valuable resource. Though perhaps not quite as engaging as Miodunka's books, "Mastering Polish" puts learners in a number of unique situations, such as the auto repair shop and an author's reading, in addition to the travel and social situations found in many foreign language textbooks. The book is accompanied with two CDs and provides students with materials to test their knowledge.
Po polsku (see resources), an online service offered by an individual speaker of Polish, presents basic information in a clear manner for beginners and covers all major grammatical points. Although the site is far from comprehensive and has many typos, it gives students a broad overview of the language.
Polish Grammar (see resources) is a good site for testing your knowledge of major grammatical points. The website provides a lot of quizzes and also features 10 lessons on grammar.
Because Polish is difficult to pronounce and has many grammatical (verbal, noun and adjectival) paradigms, it is almost impossible to master without outside help. By engaging the services of a professional teacher or tutor you can improve your speaking, listening and writing skills, have your questions answered by an experienced speaker, and have your mistakes corrected before they become deeply ingrained.
DICT (see resources) offers the best online Polish-English-Polish (it can be used in either direction) dictionary; students can enter a search term in either language and quickly see a number of related results. For home use, Larousse offers an excellent pocket dictionary with 50,000 terms.