@chrisstratton has it right; connect SWDCK, SWDIO and GND to the appropriate pins on the programmer. You'll want to use software such as OpenOCD to talk to the nRF51822 using the ST-Link interface.
I've written a lot of software for these chips; if you're doing basic blinky stuff it's not too bad but if you want to use BLE and get into their soft devices there will be a bit of a learning curve because you must flash multiple images to different parts of the nRF51822 memory. If you were using a J-Link debugger it'd be a little easier as Nordic's tools understand how to talk to these programmers and will save you some initial headaches in getting your software, the soft device and (most likely) a bootloader into the memory without erasing the previous bits you've flashed.
DevZone used to be a lot better before they redesigned everything. Now it's a bit of a crapshoot to find info you want and navigating their terrible "Web 2.0" experience drives me mad, but perhaps you'll weather it better.