The FAS3270 is available in two configurations - a single chassis HA system, or a dual chassis HA system. The single-chassis system only has two PCI slots per controller, while the dual chassis has 6. In a single chassis system, if a Flashcache/PAM card is installed, and a SAS card is installed, there are no free slots.
Assuming you have a dual chassis system, or have identified an empty slot to install the card into - failover from one controller to the other, then on the disabled controller, label any cables you need to unplug, undo the orange nut on the back, and pull the handle down to remove either the controller or the IOXM module where the card will be installed. Then remove the side panel (blue nut) and install the 10Gb Ethernet card. Re-insert the controller/IOXM, reconnect any disconnected cables, power the system back up, perform a giveback and verify the card is showing in "ifconfig" (7Mode) or "network port show" (Clustered ONTAP). The new ports will show up as eXa and eXb, where X = slot number the card was installed into. Perform this procedure to the other controller to install its card.
Configuration of the card depends on the version of ONTAP being used. For 7-Mode ONTAP, see this document and for Clustered ONTAP, see this document. OnCommand System Manager is the easiest option to use in either case. Please feel free to post any followup questions.