Obviously if your CPU fan has failed it is not advisable to run the computer.
If you can remove one side of your computer case and view the CPU & Fan from there, you will be able to see whether the fan is screwed into the top of the Heatsink. There will be screws at each corner. If this is the case, you can gently unscrew these and remove the fan (not forgetting to disconnect the power supply before doing anything). You will, obviously, need to disconnect the fan from the motherboard/power connector. You may then be able to buy and install a new fan. This is the easiest way to do the job.
The alternative is to buy a new heatsink and fan (both come together)but the spring clip which holds these to the motherboard can be fiddly and difficult to remove and install. If you are brave enough, you will need a flat screwdriver which should fit into little slots on the spring clip. You will need to press the spring clip down firmly - taking care not to slip and scratch the motherboard. To install a new hs/fan, you will need to hook the spring clip onto the little lugs again.