Even if you can log in to another account on the same system, the permissions settings for OS X will prevent you from using Finder to browse files belonging to the first account. In other words, if you're logged in and you try to open a folder that belongs to another user account, you'll get an error message telling you you don't have permission to access it. Apple has so far not made it possible in OS X to allow a Finder window opened in one account to be authenticated as a different account.

Using the root account

The root account in OS X is the main top-level account that has access to all aspects of the system, and as a result can be used to browse any files. It does need to be purposefully enabled, and bear in mind that because it has full access to the system it can be dangerous to use or keep active.

Launching the Finder under another user account

To avoid using the root account, you can instead open a new Finder instance under the name of the target account, thus getting past the permissions hurdles.(icloud sync)

While you will now be able to view the files in the account, there are some limitations to this. The Finder is built so only one instance runs at a time, and as a result its interaction with the mouse when running in this manner has limitations, so while you can browse the files in the account, delete them, and rename them, there are some things you cannot do.