The speaker wants to be able to use the "shared drive", which is shared storage space on a computer network. To use the shared drive, she needs to have a user name and a password. In other words, she needs to "get access". To "get access" means that she will be able to use it.
We use the word "access" a lot when talking about computer systems, passwords, security, information, and so on. Here are some other examples of phrases using "access":