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":

We have access to all kinds of personal information about the patients.

I will be out of the office for the week of December 27, with limited access to e-mail.

Starbucks announced that they're going to offer free Internet access at all their locations.