For the posts of permanent officials, one has to pass the selection procedure (concours). You have to apply online within a certain deadline. It can be a rather lenghtly process, but then this is public sector, with jobs for life, so and all has to be done properly & legally sound. There is no hiring from the street for these positions, and there can be tens of thousands candidates for 150 posts. the selection process only selects the "best" candidates (in terms of performance at the tests, professional experience - if required, performance at the assessment centre), who are then placed on a reserve list, from which the institutions then recruit depending on their needs.
a candidate has to speak at least 2 EU languages; some of the tests are in any of the EU 24 official languages, some in a limited number of languages (the working languages are EN/FR/DE). The tests on PC are organised all over EU, and some also worldwide. the procedure has several steps, and only the x best candidates make it to the next phase. it is a very competitive procedure, but I think it is fair as how can one assess tens of thousands of candidates with different backgrounds, different education, different languages & nationalities, if now by letting them take tests on PC (cognitive, reasoning tests). the assessment centre is quite tough, and it takes a full day.