When trying to get use to case endings, with respect to both the general rules and, often multitudinous associated exceptions, one great way to use the repetition method to get used to conjugating, is to start with sentences in full nominative - that is, in their dictionary form - and convert them accordingly to how they are supposed to be in Polish. Essentially what's required to re-render the sentence with the correct case and verb endings to match the English sentence you require.
This can be a great way to practice if you are self-teaching, because it means you can easily set yourself tricky grammar problems without even knowing it. It's also a good idea to repeat the sentence verbally once you've got the case ending right, or use an online speaking tool to produce the correct pronunciation, to get you thinking about what instances require what case endings. (Try not to repeat the sentence verbally if you get it wrong, or before conjugations have been added; you may find yourself repeating incorrect grammar when speaking!)
A great way to do this is to set up a spread sheet with the columns, 'English', 'Polish Nominative', 'Polish' and 'Case Used'. This way, you can easily see your workings if you ever come back to check what's been done in particular phrasal situations.
Polish Case - Example One
To start, write a simple English sentence in column one. Make sure it is appropriate to your level and makes sense. For our first example we'll do something really simple, with no adjectives, just a verb and subject noun: I have a dog.
In column two we write the Polish words without conjugation. We need the verb 'to have' (mieć), and the noun 'dog' (pies). So, our sentence in column two will read: mieć pies.
The third and fourth columns are the hardest, it's where you answer the question and apply the appropriate verb and noun case endings. So, once you've figured these out (here it's first person singular ['I have'] and the accusative, as we are using a transitive verb), you rewrite the nominative sentence as, Mam psa. Finally add 'ACC' or 'accusative' in the fourth column, so when you look back you can quickly remind yourself of all the associated case endings.
Polish Case - Example Two
Let's try one in the same case but add in an adjective. Something like, I like big cats.
The second 'nominative' column should read lubić duż koty. Remember here that the grammar is wrong precisely for you to alter it. To stop yourself from using examples you know you can do easily, you can use a translator tool to get the nominative form of each word individually before trying to form the correct grammatical sentence yourself.
Again, we're using a transitive verb 'to like', so in the third column our noun and adjective need to be in the accusative. We're still in the first person singular, so our verb needs to change too. The sentence should read: Lubię duże koty, and you can add 'ACC' once again to your third column.
Polish Case - Example Three
Let's try and example in a different case altogether and also stick in a preposition. How about: The cat is in the house.
So in the nominative, let's work out all the words individually and just string them together. We've got 'cat' (kot), the verb 'to be' (być), the preposition 'in' (w), and the noun 'house' (dom). Our sentence reads: Kot być w dom.
That sounds terrible, so let's quickly move on to sort out the grammar, using the required locative case and the preposition w, along with third person singular verb forms. We get: Kot jest w domu. Here we need to add 'LOC' or 'locative' to the third column to indicate the case that's been used.
Essentially using a format like this is the equivalent of 'showing your workings', it's a great way to get started on cases, particularly if you're a beginner and self-teaching learner.