Optical observatories -- or commissions that allocate time on a national or international basis to one or more telescopes -- generally accept proposals twice a year, during a one-month period with a deadline in the middle or end of March or in the middle or end of August (in both cases, these are for observations that will take place starting about six months later). The proposals are submitted via the corresponding observatory/commission web site, or sometimes via special software you have to download and run on your computer.
The specific details vary from observatory to observatory, and can best be determined by searching through their web pages and reading whatever "Call for Proposals" or "Announcement of Opportunity" document they produce. Such "Calls" are generally issued about four weeks before the deadline. (So the Calls for Proposals for the next round are mostly being issued right now.) Many observatories (e.g., Gemini North and South) are international facilities which split up their time between different national time-allocation committees, so you have to visit their pages to determine their policies. ESO is an example of an international facility with a unified time-allocation process for all the member nations (though 10% of the time is specifically reserved for Chilean proposals).
In general, people at institutions in the nation or nations associated with the observatory can always apply -- unless it's a private observatory associated with one or more institutes or universities, in which case you have to be at one of the institutes (thus most of the time at Keck is only open to people at Caltech or the University of California). Some observatories will make parts of their time available more generally; for example, in return for funding from NASA, some of the time at Keck is "open to all U.S.-based astronomers, i.e. those with their principal affiliation at a U.S. institution."
Usually observatories require at least one "eligible" person on the proposal -- and that person usually has to be the Principal Investigator for that proposal -- but the rest of the proposers can be from non-eligible institutions/countries. (Partial exception: proposals for the Anglo-Australian Telescope require that at least half of the proposers are at Australians institutions -- or else that the proposers are able to pay for the observing time.)
Here's how you can find out about ESO proposals:
If you google "eso call for proposals", you can find (at the moment) this web page, which tells you that "The deadline for Period 109 (1 April 2022 – 30 September 2022) is: 23 September, 2021". Further down on the page is a link to the actual "Call for Proposals" PDF document. Sections 4.9 ("Non-Member State Proposals") and 6.1 ("Who may submit, time allocation policies") of that document describe who can apply for time. Here you will find that groups who are not in ESO member states can still apply for time, though there is a requirement that "the required telescope/instrumentation is not available at any other observatory accessible to the applicants" -- and a note that if a proposal from ESO members and a non-ESO proposal end up equally ranked, the ESO-member proposal will get preference.
Since you say you're based in Portugal, then there's no problem at all -- Portugal is one of the ESO member states.
(OPTICON, I believe, is primarily for people in European Union states who want to use one or more of a set of 14 telescopes. A maximum of 20% of the time is available to non-EU astronomers. The current deadline for the next semester is, as I write this, about an hour and a half away, so I wouldn't worry about it right now...)
