First, note that if you're an end-user of a third party app that connects to Dropbox, you generally should not have to manually retrieve your own app key or access token. The developer should register the app themselves, and build the ability to automatically get an access token for your account into the app itself. You may wish to contact the developer to ask them to do so.
However, if the developer is requiring you to get and supply an app key or access token manually for whatever reason, you can do so by registering an app here. You may need to check with the developer or third party app's documentation to determine what settings are needed for the app.
Then, once the app is registered you can see the app key on the resulting page, and/or use the "Generate" button to get an access token for your account.