If you deleted the video yourself, YouTube can't restore it. YouTube Studio has no trash folder for videos, and YouTube's help pages treat deletion as permanent. What you can usually get back is the original file, because the YouTube copy came from something on your phone, a camera card or a computer. If YouTube removed the video and you didn't, that's a separate path, and an appeal may bring the original upload back.
Check that it's really gone
Before you search anywhere else, open YouTube Studio and go to Content. A video set to private or unlisted disappears from your channel page but is still there, and so is an upload that never left draft. Check the Shorts and Live tabs as well as Videos. If your account manages more than one channel, make sure you're signed in to the right one.
If YouTube took it down
You can appeal a video removed for breaking Community Guidelines from YouTube Studio or from the email YouTube sent about the removal. A copyright takedown has its own route: a counter notification if you own the rights or have a solid fair use case, or asking the claimant to retract. Either way, the original upload only comes back if the decision is reversed, so keep any local copy safe while you wait.
If you deleted it: find the original file
Most recoveries actually happen here. Go through the places the file passed on its way to YouTube.
Start with your phone, if you shot it there. Phone photo apps keep deleted items in a recently deleted album for a limited time, and a cloud photo backup may still have a copy after that.
Then your computer. Look in the export or render folder of whatever you edited with, and in the trash or recycle bin. If the editing project still exists, its timeline points to the raw clips, and you can export the video again even if the final file is gone.
Then drives and cards. External drives and old camera cards often still have the raw footage. If files were deleted from a card and nothing has been recorded over them since, file recovery software can sometimes bring them back, so stop using the card until you've tried.
Then other people. An editor, a collaborator, or anyone you sent a review copy to may still have the file.
Often the file is there and you just can't tell which one it is, because it's called something like final_v3 and sits next to other versions. When the raw footage is spread across several shoots and you only remember what happens in the video, you can upload that batch to a Vivu project, describe a moment from it, get back time ranges you can open, and export the original clips to rebuild the edit. It searches files you upload, not YouTube links, so it can't pull the deleted upload itself back. Some matches will be loosely related, so expect to open a few before you find the right shoot. The same kind of digging through old material is covered in going back through a back catalog.
If you don't have the file anywhere
Then you're looking for copies other people made. Search the video's old URL in the Internet Archive's Wayback Machine. It archives some video pages, but the video itself is often missing or low quality. Search the title on YouTube and elsewhere for reuploads, since popular videos get copied. Old links, notification emails and embeds on your own site will give you the exact title and video ID to search for. Be wary of sites that claim they can restore deleted YouTube videos. All they can do is show you copies that already exist somewhere.
Google Takeout won't help here either. It exports the videos currently on your channel, not ones you've deleted.
When you don't need any tool
If the exported file is sitting in your downloads or export folder, re-upload it and you're done. A re-upload is a new video with a new URL, though. The old views, comments and links don't carry over, and anything that pointed to the old URL needs updating. Searching your footage by content is only worth it when the file you need is buried among many recordings with names that tell you nothing. The cheaper fix for next time is a habit of keeping exports and naming them, which keeping footage findable across years goes into.
Where this leaves you
If YouTube removed the video, your job is the appeal. If you removed it, your job is finding the file you uploaded from, and that comes down to how many places it could be and whether you'd recognize it by name. A few folders and a clear export name mean you'll find it by hand. Years of raw footage under generic filenames is the case where searching by what's in the video starts to make sense.
FAQ
Can YouTube support restore a video I deleted by mistake?
Generally no. YouTube treats a creator's deletion as permanent and has no restore option in YouTube Studio.
The realistic way back is re-uploading from the original file on your phone, computer or drives, or from a copy someone else kept.
Will I get my views and comments back if I re-upload?
No. A re-upload is a new video with a new URL, so it starts with no views or comments, and old links and embeds still point to the deleted video.
A video YouTube removed is different. If your appeal succeeds, the original upload is reinstated.
Can I recover a deleted YouTube video with Google Takeout?
No. Takeout exports the videos still on your channel. Once a video is deleted, it isn't part of the export anymore, so Takeout is useful as a regular backup, not as a way to recover something.
How do I find a deleted YouTube video if it wasn't mine?
Search the old URL in the Wayback Machine and look for reuploads by searching the title. Archived pages often don't include the video itself, and reuploads may be cropped or lower quality.
If you know who uploaded it, asking them directly is often the only way to get the original.