The UN recruitment process is fairly standardized. You submit your application online using a corporate tool for that purpose. If the hiring manager finds your profile interesting you may be invited for a written test (did not happen in this particular case, but in others), the next step is one or more competency based interviews (the UN has a defined set of competencies with clear criteria). In this case I had a Skype interview, which is rare. More common are phone interviews or video-conference interviews (if the hiring duty station is different than where you currently are) or on-site interviews (if you can travel). In very rare, exceptional cases you may be invited and travel will be paid by the organization (this happened to me only twice). Follow-up interviews may happen, but are also rare. The recruiter would then decide whether you are a good fit for the job (which could be more than one candidate) and put you on the "recommended list". This list is then submitted for internal review by appropriate bodies. The approved recommended list will then be returned to the head of the department for the selection of one candidate (the head typically follows the recommendation of the hiring manager). Other candidates on the recommended list are placed on a roster for similar positions. The selected candidate is informed.
The main drawback is that this process can take a very long time. Rarely it is quicker than 6 months and there are situations where recruitment took almost 2 years for a single position.