How do I transfer files from my old PC to the new one without losing anything?

Actually, "without losing anything" is kind of risky to guarantee, because there's always a chance something could go wrong along the way. The safest bet is to use an external hard drive or a big USB drive to back up your important files (documents, photos, videos), then transfer them to the new PC via USB cable or even over the network if both have wifi. If you want to transfer everything at once (system, programs, and all that), then you need specific software like Acronis or Macrium Reflect, which clones the entire disk, but even so it's good to have a separate backup of your critical files just so you don't get left in the lurch.

I disagree that it's just about backing up to a USB drive or external hard drive - you can do a direct transfer, actually, using an ethernet cable or folder sharing if both PCs have access to the same network. Sure, doing a backup first is always smart (nobody's arguing with that), but you can move the files and keep everything in place without relying only on a USB drive. If the PCs are too old for the network to work properly, then yeah, an external hard drive gets more practical, but in most cases it works fine over the network itself.

What's the total size of the files you need to move? Because depending on that, the best strategy changes quite a bit.

The most practical way is to connect both PCs directly to the network and do the transfer via folder sharing - it's way faster than a USB drive or external hard drive, especially if there are a lot of files. If both are on the same WiFi or connected by network cable, you open File Explorer on the new PC, type in the address of the other computer (like \\COMPUTERNAME\users) and you can access the folders from there. After that it's just copy and paste, really simple.

But there's a trick that a lot of people don't do and should: before moving anything, back up your important files to an external hard drive or the cloud, like OneDrive or Google Drive. It's not so you can delete them later - it's just to have a Plan B in case something goes wrong during the transfer. Then you transfer over the network, verify that everything arrived correctly on the new PC and only after that delete it from the old one. That way you can sleep easy knowing you didn't lose anything even if the process had some issues.