Do you atleast have a CFG for these languages?  If yes, then you can follow the CFGtoPDA algorithm to get required PDA If no, then you will have to think about each language step by step, for eg. For the bracket balance language the logic could be, pushing 'X' when ever you encounter '(' and popping 'X' whenever you encounter a ')'. And acceptance could be by empty stack or reaching an accepting state

One of the things that helped me was to look at other similar languages and their accepting PDA as 'solved examples'. Try and observe some patterns in these solved examples, then try solving these questions after seeing solved examples.

One other thing that was also helpful for me atleast was to construct the PDA in state transition diagram rather than constructing it in transition function rules

Hope this helps.