Cases, cases, cases. It's the word that's flung around most by Polish language teachers, and indeed the Polish themselves, often as evidence for the intense difficulty of their native languages’ constituent grammar. After studying Polish for some time as an isolated student, I was lucky enough to be able to relocate to the country itself. Allowed that greatest, and perhaps, most daunting of practice tools, immersion, I discovered that hours spent nose down in a Polish Grammar textbook was at best going to give me a good understanding of grammatical cases and when they should be used, but never the confidence or experience-backed knowledge to give it a shot in conversation. It's true actually that even if you don't get all the particular case endings dead on, you can at least get the ending in the right ball park so to speak, and still go a long way to making your sentences intelligible to native speakers.
The best way I found to do this was to replace classroom grammar study with conversation - using my vocabulary as much as I could, but always bearing in mind that I couldn't ignore grammar altogether. Eventually, you'll start getting it right precisely because you once got it wrong, and while you may not have textbook grammar, the multitude of exceptions wrapped up in this subject means that it can and will only come with time.
That said, I did find that supplementing my language learning with some particular grammar studies meant that when it came to translating my work into practice (conversation), I was armed with a little more confidence. In particular getting used to this list of common noun phrases or sentence structures, will give you a much better arsenal when it comes to deciding what noun/adjective case endings to attempt.
Noun Phrases and Their Appropriate Case
Perhaps the most common noun phrase usage is as the simple subject of a verb, and for this, in Polish, we use the nominative case ('Asia uczy się' ['Asia studies', where 'Asia' is in the nominative].
We can also place nouns as the object of a transitive verb (this is also known as the direct object), and for this we use the accusative case ('Mam starszego brata' [I have an old brother, where 'starszego brata' is in the accusative).
When we use the existential verb być ('to be') we always use the nominative case for our noun subject (pies jest, 'the dog is here'), unless you are expressing negation, in which case we use the genitive (psa nie ma, 'the dog is not here'). This is also true for expressing negated forms of transitive verbs (nie mam psa, 'I don't have a dog', where 'psa' is the subject in the genitive).
For possession we also put the subject noun in the genitive case (dom mojego brata 'my brother's house').
The phrasing of nouns varies greatly with the use of a preposition. The case depends on what verb and preposition combination is used in the sentence, and there are a multitude of correct forms here, so it's worth keeping your ears open to pick up which verb/preposition/case combinations occur in conversation. Some common examples are 'czekam na + accusative' ('I wait for', where the object is in the accusative), and 'zrobił to dla + genitive' ('x made it for', where 'x' is the subject and the object is in the genitive).
With locational prepositions (that is a preposition that indicates where something or someone is physically), it's usually the aptly named locative case (Asia mieszka w Warszawie, 'Asia lives in Warsaw', where 'w' is the locational preposition, and 'Warszawie' is the subject in the locative).
These are some of the most common noun phrases; getting to know which case you should use in each will cover most bases in general conversation and mean you can really put your case ending knowledge to the test when speaking to natives.