Zaimki (Pronouns)

As compared to the numeral or the verb, the pronoun is quite friendly and easy to remember. Once you've mastered the cases, you should have no problem learning the pronouns. Well, almost no problem, since it's still Polish we're talking about and of course there's some exceptions on the way.
Let's have a quick look at the types of pronouns in Polish

1. Personal Pronouns

• singular: ja, ty, on, ona, ono

• plural: my, wy, oni (all male & mixed male-female groups), one

Note that ja, ty, my, wy are usually not expressed as subjects, unless emphasized. Thus, we will say:
Czytamy, instead of My czytamy, because the verb gives us full information about the person.

• You must remember the polite, formal address as well, because this is the form you'll be using when talking to Polish people, at least for the beginning. If you use ty when talking to someone you've just met, you might be considered rude. However, you'll switch from formal to informal rather quickly, most of the times after a "ceremonial" caled bruderszaft, which involves drinking some vodka and kissing each other on the cheeks. The act of changing from the polite form to a more friendly "you" must be acknowledged by both parties. Also, when talking to someone older, they must be the ones to suggest giving up formal address.
• singular: Pan (masc), Pani (fem)
• plural: Panowie (masc), Panie (fem), Panstwo (masc&fem)

2. Possessive Pronouns

• they take a full set of agreeing endings and act like adjectives - they have the same type of declension
  

3. Demonstrative and Relative Pronouns

• Polish language does not have the category of "article", therefore you will understand from the context if a certain noun is definite or indefinite. Demonstrative and relative pronouns have full case-and-number declension

4. Reflexive pronoun

• it means "oneself", "each other", "one another" and it has no Nominative case form

5. Distributive pronouns

• they are matched by different pronouns in the plural and in expressing negation, but they all function like adjectives and have full case-and-number declension.

You'll probably have to learn the personal pronouns as they are - and worry not if you don't remember all forms, once you start speaking they will all come naturally, and you'll end up wondering why you spent all that time and energy trying to learn something that was so obvious. For the rest of the pronouns, all it takes is good command of the cases.
Here's a chart with declension patterns for the above-mentioned pronouns.