Blue Screen When I Load Into a Game

So I play League of Legends regularly, and recently have been getting blue screened every time I load into a game. I can do other things on my computer without issue, but once I load into a game I get a blue screen. If someone could walk me through the steps required to diagnose my problem then that would be ideal. I assume you'll ask for my PC specs so I'll go ahead and list them, any response is appreciated.

HDD : SAMSUNG Spinpoint F3 ST1000DM005/HD103SJ 1TB 7200 RPM 32MB Cache SATA 3.0Gb/s 3.5" Internal Hard Drive - Newegg.com
DVD: ASUS Model DRW-24B1ST/BLK/B/AS 24X DVD Burner - Bulk Black - Newegg.com
Mobo: MSI 870-G45 ATX AMD Motherboard - Newegg.com
GPU: MSI R5770 Hawk Radeon HD 5770 1GB 128-bit Video Card - Newegg.com
PSU: Thermaltake TR2 W0070RUC 430W ATX12V V2.2 Intel Core i7 Compliant Dual 80mm Fans Full Cable Sleevings Power Supply - Newegg.com
RAM : Crucial Ballistix Sport 4GB (2 x 2GB) 240-Pin DDR3 SDRAM DDR3 1333 Desktop Memory Model BL2KIT25664BA1339 - Newegg.com
CPU: AMD Phenom II X4 840 3.2GHz Socket AM3 95W Quad-Core Desktop Processor HDX840WFGMBOX - Newegg.com
Case: NZXT M59 - 001BK Black Steel ATX Mid Tower Computer Case - Newegg.com