You are reading right, we have the first monthly cumulative update package for SharePoint Server 2013 and all the other Office 2013 products.

In case you saw the security fix updates first: http://support.microsoft.com/kb/2980001 please remember that the CU packages below are containing the changes you could install with the security or public update (PU).

Be aware that all Updates for SharePoint 2013 require March 2013 PU for SharePoint 2013 to be installed first or our recommendation is to have SP1 installed.

SharePoint Foundation 2013
2882999 The full server package for SharePoint Foundation 2013
http://support.microsoft.com/default.aspx?scid=kb;EN-US;2882999

Download link: http://support.microsoft.com/hotfix/KBHotfix.aspx?kbnum=2882999&kbln=en-us

SharePoint Server 2013
2882989 The full server package for SharePoint Server 2013 and contains also the SharePoint Foundation 2013 fixes so you need only this package.
http://support.microsoft.com/default.aspx?scid=kb;EN-US;2882989

Download link: http://support.microsoft.com/hotfix/KBHotfix.aspx?kbnum=2882989&kbln=en-us

You will see three downloadable packages:

image

You need to download all three and put these into the same folder, before you start the installation.

Office Web Apps Server 2013
2883003 Microsoft Office Web Apps Server 2013 hotfix package    
http://support.microsoft.com/kb/2883003

Download link: http://support.microsoft.com/hotfix/KBHotfix.aspx?kbnum=2883003&kbln=en-us

Project Server 2013
2882990 The full server package for Project Server 2013 and contains also the SharePoint Server and Foundation 2013 fixes so you need only this package.
http://support.microsoft.com/default.aspx?scid=kb;EN-US;2882990

Download link: http://support.microsoft.com/hotfix/KBHotfix.aspx?kbnum=2882990

You will see three downloadable packages:

image

You need to download all three and put these into the same folder, before you start the installation.

Important for all Server Applications listed above:
After applying the preceding updates, run the SharePoint Products and Technologies Configuration Wizard or “psconfig –cmd upgrade –inplace b2b -wait” in command line. This needs to be done on all servers in the farm with SharePoint installed. You can run psconfig in parallel on all SharePoint machines.

You might have you own strategy to run psconfig because it depends on the farm structure and what makes sense to reduce the downtime.

Related Info:

Update Center for Microsoft Office, Office Servers, and Related Products
Common Question: What is the difference between a PU, a CU and a COD?

CHANGE: SharePoint 2013 Rollup Update for the December 2013 Cumulative Update Packaging

How to: install update packages on a SharePoint 2013 farm where search component and high availability search topologies are enabled

SQL Server 2014 and SharePoint Server 2013