Can I connect my Mid 2011 Mac to a second monitor? How can I connect my mid 2011 iMac to a second monitor to extend my screen? The monitor is an HP L1950. The ports my mac has can be seen here:
Your iMac has a Thunderbolt 2 connector which also acts as a Mini DisplayPort. 
Since your Monitor supports (15-Pin D-Sub) VGA or DVI-D you either need a Mini-DisplayPort to VGA or to DVI-D cable. I would recommend getting a DVI-D (e.g from Amazon, your local store might have one of the mentioned options as well), since it is the newer and slightly better standard, though VGA is (for old) equipment more common.

In general though, this is old Hardware and HDMI is more or less standard now.