I would like to start off with getting prepared for postgraduate applications to study abroad. Yes, you need to invest in yourself before applying for it. What do I mean by investing in yourself? You should be active and build your CV by the time. For instance, get involved with projects in your department with a professor whose researches you like, do an internship abroad, part-time work while studying, be a volunteer, and be a part of society. These examples will help you to improve yourself and bring you the required connections for future applications.
While you are growing yourself, start off researching the programs and universities you are interested in. Continue with obtaining the requirements of the programs. For instance, it might be an English proficiency exam such as IELTS or TOEFL. English is not like Math or Chemistry, you cannot have it in a couple of days. From my experience, the requirement is starting with 6.5 out of 9 for IETLS and 90 out of 120 for TOEFL, however, this differs for universities. (Examples for IELTS requirement: Carleton University :6.5, Cambridge: 7.5 and Edinburgh Napier: 6.5) Improve it by putting effort into it. It could be Graduate Record Examination (GRE) which is mostly asked by universities around the US and Canada. Start working on them.
I got some questions such as what are the qualifications needed to have while applying for a Master's or Ph.D.? In my opinion, your research potential and GPA are the foremost attributes they are looking for. Secondly, the relevance of the program you are planning to apply to and your department. For instance, you might be an electrical engineer planning to apply for a computer science program. Thirdly, your extracurricular activities such as taking participate in the Erasmus+youth exchange programme, being a member of society. Lastly, the references. From my experience, if you do know someone close or well known by their works to the supervisor you would like to study with, then yes that's one of the vital qualities. Other than that, references are not as strong as your GPA and research ability. Still... they are important.
I hope this will help you and answer your questions. If you have more questions, please write them in the comments. I would be so glad to help you out, guys!