Basic word order in Polish is SVO, however, as it is a morpheme rich language, it is possible to move words around in the sentence, and to drop the subject, object or even sometimes verb, if they are obvious from context.

These sentences mean more or less the same (“Kasia has a cat”), but different shades of meaning are emphasized by selecting different word orders:

Kasia ma kota – Kasia has a cat (when spoken with a different sentence tempo and accentuation, this sentence can be understood as mildly offensive idiom “Kasia is crazy” or “Kasia is a loony”).

Kasia kota ma – Kasia does have (own) a cat (and has not borrowed it)

Kota ma Kasia – The/a cat is owned by Kasia

Ma Kasia kota – Kasia really does have a cat 
Kota Kasia ma – It is just the cat that Kasia really has
Ma kota Kasia – The relationship of Kasia to the cat is one of ownership (and not temporary possession)
However, only the first three examples sound natural in Polish, and others should be used for special emphasis only, if at all.

If a question mark is added to the end of those sentences they will all mean “does Kasia have a cat?”; an optional ‘czy’ could be added to the beginning (but native speakers do not always use it).

If apparent from context, the subject, object or even the verb, can be dropped:

Ma kota – can be used if it is obvious who is the person talked about
Ma – short answer for “Czy Kasia ma kota?” (as in “Yes, she does”)
Kasia – answer for “Kto ma kota?” (as in “Kasia does”)
Kota – answer for “Co ma Kasia?” (as in “The cat”)
Kasia ma – (as in “Kasia does [have one]”) answer for “Kto z naszych znajomych ma kota?” (“Who among people we know has a cat?”)
Note the interrogative particle “czy”, which is used to start a yes/no question. The particle is not obligatory, and sometimes rising intonation is the only signal of the interrogative character of the sentence: “Kasia ma kota?”.

There is a tendency in Polish to drop the subject rather than the object as it is uncommon to know the object but not the subject. If the question were “Kto ma kota?” (Who has a/the cat?), the answer should be “Kasia” alone, without a verb.

In particular, “ja” (I) and “ty” (you, singular), and their plural equivalents “my” (we) and “wy” (you, plural), are almost always dropped.

Word order in Polish tends to reflect the increasing informational prominence of the elements in a sentence as one proceeds from left to right. Items placed at sentence-end typically carry logical stress and respond to the implicit question statement answers. For example, in Janusz kocha Marię. Janusz-nom. loves Maria-Acc. the sentence answers the question “Whom does Janusz love?” (Maria). The same sentence with the subject and object reversed Marię kocha Janusz. (in effect, “Maria is loved by Janusz.”) answers the question “Who loves Maria?” (Janusz). Polish often makes use of the device of subject-object reversal to express what the equivalent of passive voice is:

Obudził mnie telefon. I-Acc. was awakened by the telephone-Nom.

Background information is typically placed in the first part of a sentence. Note the difference between Polish and English in this regard:

Jutro wieczorem w tej sali odbędzie się zebranie dyrektorów. There will be a meeting of directors in this room tomorrow evening.

Manner adverbs in Polish tend to be placed earlier in a sentence rather than later. Note here too the difference between Polish and English:

On dobrze mówi po polsku. He speaks Polish well.

Again, if you do have questions, please let me know in comments below.

Do następnego razu! (Till next time…)