You just need to install Dropbox on the new computer and then enter your username and password when prompted.
The Dropbox application will begin downloading the files in your Dropbox folder for you automatically once you log in while you should be able to boost the syncing process up by changing your bandwidth settings.
If you already have your Dropbox folder somewhere else and you want to move it to the new computer without downloading everything from the website, please refer to the instructions in the following Help center article:
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