You can make an SD adapter pretty cheaply. Google DIY SD card
If your Arduino is 3.3V then you don't have to do any voltage leveling, otherwise you will need a small handful of cheap parts for leveling.
The neatest voltage leveling I've seen uses 3.3V pullups on the SD adapter input pins and diodes on the same pins blocking 5V input. It only wastes a little power on one line.
When a 5V line is HIGH, the SD card reads 3.3V HIGH pullup because the diode blocks the 5V.
When a 5V line is LOW, it takes the pullup current away through the diode and the SD card reads LOW.
Feed the SD card VCC from a voltage divider and use that same line to power the pullups through 10k resistors.
That's 2 resistors for VCC and a resistor and diode for MOSI, SCK and SS.
However you wire it, there are oodles of voltage leveling circuits and chips, the code will be the same.
In your IDE under File->Examples-> you should find the SD examples and they should run.