Download Memtest86+ here:
Memtest86+ - Advanced Memory Diagnostic Tool
Which should I download?
You can either download the pre-compiled ISO that you would burn to a CD and then boot from the CD, or you can download the auto-installer for the USB key. What this will do is format your USB drive, make it a bootable device, and then install the necessary files. Both do the same job, it's just up to you which you choose, or which you have available (whether it's CD or USB).
How Memtest works:
Memtest86 writes a series of test patterns to most memory addresses, reads back the data written, and compares it for errors.
The default pass does 9 different tests, varying in access patterns and test data. A tenth test, bit fade, is selectable from the menu. It writes all memory with zeroes, then sleeps for 90 minutes before checking to see if bits have changed (perhaps because of refresh problems). This is repeated with all ones for a total time of 3 hours per pass.
Many chipsets can report RAM speeds and timings via SPD (Serial Presence Detect) or EPP (Enhanced Performance Profiles), and some even support changing the expected memory speed. If the expected memory speed is overclocked, Memtest86 can test that memory performance is error-free with these faster settings.
Some hardware is able to report the "PAT status" (PAT: enabled or PAT: disabled). This is a reference to Intel Performance acceleration technology; there may be BIOS settings which affect this aspect of memory timing.
This information, if available to the program, can be displayed via a menu option.
Any other questions, they can most likely be answered by reading this great guide here:
FAQ : please read before posting