Once you are in the system, you should have no trouble accessing the file server and downloading the file you need. (Use the file copier and download the file 'uplink test data' into your memory banks). In many cases this might not be so easy - you may find that Firewall of Proxy systems are running, which will prevent you from just copying files easily. You will learn to bypass these in time.
Once you've got the file, disconnect from the system as soon as possible. You can now send it to the employer (by clicking on 'reply' in the mission screen) and receive your payment, which in this case will be zero (it was only a test after all).
The File Copier program is one of the two programs you start off with for free. These come in all the new Agent accounts to help a new agent start earning some credits.