If you chose to replace your cooler, use a cooler approved by the processor manufacturer. If you intend to Over Clock your new CPU you may be exceeding its TDP and require more cooling. Buy the best cooling solution you can. Shown in the last photograph is a friend's Noctua cooler as you can see it has massive heat dissipation capacity. I fitted a CNPS9900
Place the cooler on the CPU. Attach the bracket without the locking mechanism to its notch first then an attach the other side. Ensure both sides are attached, push the tension leaver into the locked position.
Once you have re-assembled your PC and powered it on you may be prompted to go into Setup/BIOS to save the new hardware configuration. If you have set any static voltage or timing values for the old CPU you may need to changed them or set them back to auto.
For Windows machines you can download a free utility to check temperatures and voltages: HWMonitor
For Linux machines you can use I-Nex to check temperatures and voltages
