On Leonardo and Due SD Card breakout has to be connected to SPI. SPI is not available thrue normal female headers but the ICSP Header on rear center of the board. Avoiding to search for pins every time I connect it, I created my SPI-Adapter for Leonardo.
What you need is some small rest of PCB, 6 pin header and cable for the connection. Some wire. Your solder iron 2pin female header, 8pin female header.
Solder your pins and headers to the board as shown in the schematic to the board. Then wire and solder them them as shown.When done you connect CS-pin from breakout to D4 on your Arduino. Hook the breakout board on yor adapter and connect it to ICSP. More information on Adafruits product page.
Nice thing is. This works on DUE as well. Just connect it to your SPI header and go.
Since the comment option does not like me I add my comment here:
The perfboard is from Conrad and comes really handy. No need to cout strips.