You will need to get to the Backend Pages and then edit the Dashboard.
Unfortunatelly the Dashboard is a single control thing so you can't remove parts of it. You either remove the whole Dashboard control or leave it intact. No customizations on it as far as I see.
If you are still going to remove the Dashboard and add your own content there - follow these steps:
1. Go to Settings
2. Select "Backend Pages
3. Confirm you know what you're doing on the Caution screen.
4. Expand the Sitefinity node in the pages screen and click edit on the Dashboard page.
You will be in Page edit for the Dashboard page. Unfortunatelly as I said - you're not going to be able to just remove bits of it and leave other bits, you either remove it or leave it.
Caution: Please either get the website backed up (the database mainly) or be extremelly careful as you really can mess the things up. I am not quite sure if you can restore the Dashboard widget in case you want to without having a database restore. This makes it a bit difficult if you're website is live. I suggest doing this on a local website first to check how it is going before doing it on a production website.
Caution 2: In case you screwed the dashboard - you are likelly to land on a page with (depending on how much you screwed it) no menu so your backend may be inaccessible as you have no menu to choose items from. If you loose youre menu, navigate directly to a page other than the dashboard in order to have the backend menu (like http://yoursite/Sitefinity/Pages or http://yoursite/Sitefinity/Administration/BackendPages).
P.S. I added 2 screenshots to help you get to the Dashboard edit page.
P.P.S. We (here @eVeliko
) are working on something that may be appear helpful in situations like this but I'll keep it secret until at least the trial gets out so be sure to check the marketplace on a regular basis (sorry for the marketing ;).
Let me know if you need some more help.