There could be some more information in your question to help us answering it. Ideally, which Operating System (OS) you have (Windows? any Mac?).
And if I understood correctly, you have a pendrive (flash drive) with some sensitive / important files on it, and it's connected to a computer during some time. And you want to know if someone, using that computer, did copy, move, etc., files from or to the pendrive.
In general, you can't know. Just some OS have ability to create a log of this kind of activity. In those systems, you enable logging for all files access that is made, and then you can erad the log to see if something was read. I'm assuming that you are using Windows home-edition...
To avoid loosing information from your pendrive (someone deleting), the protection is to have a backup somewhere else.
To avoid having sensitive files read from it, the solution is to protect those files with some encryption, so that anyone who copies the file won't be able to read its contents. For example, you can password protect Word / OpenOffice files, you can zip your files using password protection, you can use Truecrypt to create a virtual protected drive inside your pendrive...
Give more details on what you need, and people will be able to give better ideas.