The official website (.app), the forum site, the dev builds site and the API have all been taken down due to legal issues however there is a workaround with official builds for all OS hosted at https://popcorn-time.ga/build/
First step for any issue is to make sure you are running the latest official version, if you are not, or just aren't sure, you can find it at https://popcorn-time.ga/build/ (currently version 0.4.7 for desktop and version 0.3.4 for Android and AndroidTV). There are also other apps using the same name, if your app looks like this or this or this, shows popups or asks for money its not our version. Download the official app or find support for your app on its own forum/site/subreddit.
Go to Settings, find the API server section and select one of the suggested APIs from the popup menu that is displayed when you click a Custom API field then restart the app when prompted. If after changing the API you get the following message "The remote movies API failed to respond, please check (chosen API link) and try again later" then try and open the link directly in your browser. If it doesn't open then your ISP is probably blocking so you'll need to try the app with a VPN. If you know of any other compatible APIs they will also work. To change back to the default API just clear the relevant textbox and restart the app again. (*unfortunately there are no known compatible Anime APIs at the moment. If one exists in the future, or support is added for an existing but not compatible one, it will be added here as well as in the suggested API list in the app)
Use the search function in the Torrent Collection page. You can also copy/paste or drag/drop magnet/torrent links from other sites in the app. If it's a series then search for a full season torrent instead of individual episodes, they are usually better seeded.
If the movie/episode has good health (green dot) then something is blocking the connection. It might be something locally on your system/network or it might be your ISP in which case you might need a VPN. If you already have a VPN make sure you are connected to a server that supports p2p. If the movie/episode has bad health (red dot) then use the Torrent Collection as detailed above. You could also try enabling 'Protocol Encryption' in the settings, it will allow you to connect to more peers (any that also use PE/MSE) but might also result in increased CPU usage and/or UI lag spikes.
It might be that OpenSubtitles.org is having issues or doing maintenance. If they are not or if this continues for an extended amount of time, or if you just want, you could try creating an OpenSubtitles account and connecting with it in Popcorn Time's settings. It should solve some issues an unregistered user might have.
This is only a reminder / advert to use a VPN which can be removed by unchecking 'Enable VPN' in the Settings. If you have your own VPN it will still work with the app.