Follow this guide in order to replace the hard drive to your Dell Latitude E6510.
Unlock the two latches on the back by sliding them inwards.
Slide the battery out from the laptop.
After removing the battery, unscrew the four 3 mm screws on the back plate using a Phillips #1 screwdriver.
The hard drive should slide out of the laptop. However, if not, use a spudger to pry the hard drive out of the laptop.