Note: By mentioning olympiads anywhere on the website, I refer to these rather than the silverzone or SOF ones. Read the last section for better distinction.
I am familiar with the selection process of only Astronomy/Astrophysics, Biology, Chemistry, Junior Science, Mathematics and Physics. The others mentioned on wikipedia also have similar reputation as these but have a slightly different selection procedure (not through HBCSE)
For PCAB and JS, the first stage is NSEs. IAPT is the organization which conducts NSEs, so check their website for registration. These happen around the end of November. These are usually objective. For Mathematics, the first level in Pre-RMO, followed by RMO. For registration in Pre-RMO check this website. Around some hundred students qualify for the next level, INOs.
This is the next stage and HBCSE organizes it. These are usually subjective and happen near the end of January or the start of February. Around 30-50 students qualify for the next stage, OCSC.
These are orientation-cum-selection camps where all the qualifying students are invited to HBCSE, Mumbai. These range from week long to month long depending on olympiads and are the most awesome parts of olympiads (in my opinion). There are amazing lectures by amazing professors. It is a once-in-a-lifetime opportunity. However, because it’s a selection camp, there are (many) tests which decide the 4-6 student team which go on to represent international olympiads.
This is not a selection level. It is pre departure camp where the team comes at HBCSE before the international olympiad to prepare and revise all the concepts, topics, etc. The whole team then departs for the olympiad HBCSE itself.
This is the final level, where your team is accompanied by 2 team leaders and 2 observers who are mostly professors who taught you in OCSC to a ‘trip’ to the country organizing the olympiad. This is, obviously, the most fun part. You get to meet amazing people from all over the world, make international friends, have fun playing games with all the other participants, and making life-lasting memories. There are also exams, but I am not emphasizing them as I feel the purpose of olympiads is the former. Surely, you are gonna love the week.
You can check out what helped me in IOAA, IMO, IJSO, or other levels of Physics and Chemistry olympiads through the below links:
The initial levels are as important as the final ones. NSEs and INOs help a lot in improving problem solving skills, and I feel, inculcate some research skills. On the other hand, OCSC and International Olympiads are an awesome way to connect with amazing kids all over the country and world. Also, they are quite representative of which students you will find regularly in the ‘top 10/100’ list of all the major exams. I met with more than 50% of students in JSO-OCSC multiple times at various camps, exam centres, learning programmes, etc and I am still connected with many of them as ‘best’ friends till now(as of 2021). I am also connected with most participants in IOAA 2019, and many of them are my friends (and even podmates :)) at MIT.
Distinction from other ‘olympiads’
There are many other exams which are also titled as ‘olympiads’, like the SOF-NSO or SOF-IMO. I will not go into the discussion whether they are ‘actual’ olympiads, because that is just the issue of definition. However, the SOF ones or any other ‘olympiad’ are pretty different from the ones I am referring to. They don’t have the “team representation”, that is no team goes on to an international event to ‘represent’ India and, I feel, the difficulty of questions is not as high as the above ones. Even though I would recommend taking the SOF olympiads, as it helps in testing your problem solving capacity, time management, etc(I took every SOF-NSO, SOF-IMO, SOF-NCO till grade 12 and got decent prizes), but don’t expect it to be recognized as a significant international achievement at elite colleges. Most professors at MIT know about international olympiads, but I doubt they would know about SOF ones. Again, this is my personal opinion, but most people I know share the same.