First, some basic vocaboulary. Weaboos will know this already - there's hard subs and soft subs. Hard subs are encoded directly into the video, they're part of the frames. You can't turn them off and are considered kinda bad quality. They're harder to find nowadays. Soft subs are your best friends! They're captions that you can turn on and off. For them, you need a media player software that support subs (like VLC). They can be inside the video (usually when the videos is in .mkv format) or outside the video, as files of their own, in .srt format mostly. To get VLC to play an external subtitle file automatically, you need to rename it with the same name as your video file (ex: snails.mp4 + snails.srt), and they need to be in the same folder.

The easiest way to get subs is to just look for a video that includes subtitles from the get-go. I'm gonna walk you through the steps in 1337x, but this will work in other torrent sites as well! Usually, searching for "movie name sub" will get you few or no results - most times, it's movies with multiple dubs (for example, multiple spoken languages you can choose from) that have subs for each language. However: internal subtitles are often a sign of quality, and many good/quality releases will include them!

So. Let's say you want to watch the Fellowship of the Ring:

It's a popular movie, and there's a lot to choose from. No mention of subs, but... The first two super popular ones - they're so popular because they're from YIFY. Their releases are TINY compressed, and you will lose some quality, but get tiny files that are easy to store and process! In my experience, it's a dice roll whether they'll have subs, but since they're so popular, you can usually download external matching subs from yts-subs.com. Let's open the first one up. You want to look for info about the "video", "audio", and next possibly "text", "subs", or "subtitles" tracks, and... bingo!

There's English subtitles in this one! What about the third one, that's 14.7 GBs?

I had to press ctrl+f on my browser to search for keywords, since it was a lot of text... but see how it says "Text#1", "Text#2", etc? They're describing in detail the quality of the subtitles! LOTR is a very popular saga, so releases tend to be very good for the average user.

Same method can be applied for tv series. Usually, the best the rip quality, the higher the chances they'll have subs.

Same season of doctor who - first one is half the size as the second one (lower quality), but no subs to be found on the first one.

What if you don't find a torrent that includes subtitles? Or if you don't have the storage space to download the fancy ones?

There's websites where you can look for your video file, and see if someone has uploaded subtitles for it.

I already mentioned the YIFY subtitles site, for subs for YIFY releases, yts-subs,

opensubtitles is a bit clunky in UI, but very good for movies,

addic7ed is the best for tv shows,

I've also heard good things of subscene.

It's best to look for subtitles that match your release/filename perfectly, as they will be synced better. But if you have subs that are out of sync, you can usually adjust them in VLC directly (usually just pressing g or h until they look good is enough). This easy technique saved my ass a lot.

Lastly: even though I don't use them myself, there are media players (and possibly VLC plugins?) that retrieve subtitles directly from online sites so you don't have to go hunting for them. I just gave BSPlayer a shot rn - it's super pushy in wanting you to get the paid option, and I don't like the UI, but it doesn't bundle adware or anything like that, and does it's job! Once you open a video file, you go in "menu>subtitles>check for subtitles online" and you can try them on, see which one works the best.