Mojang Support will give you extensive help but here are the main steps that you need to follow. Please be cautious with moving or modifying these files. It is advised that you to make a backup before you perform any actions in this folder. You can back up your files by copying them and storing them in another folder or on a USB drive.
Start by finding your saves folder. You can find all Minecraft folders, including the saves folder, by going in to the game launcher:
- Open the Minecraft launcher and log in. Choose the option "Edit Profile" in the bottom left corner. Find the button named "Open Game Dir" located at the bottom right side of the Profile Editor. A new window will open containing your Minecraft folder. When you open the saves folder you will see all your saved worlds in different folders
- Place the world folder(s) that you want to transfer onto a portable storage device, file sharing software or cloud computing service.
- Once the files are ready to be transferred, place them in the new computer's saves folder and they will be available in your list of singleplayer worlds.