Eggs should be kept at a cool and consistent temperature, preferably below 20C, which helps to minimise the growth of any micro-organisms that may be present. The best way to avoid temperature fluctuations, and thus the best way to keep your eggs fresh, is to keep your eggs in the fridge. Furthermore, I would always recommend that you keep your eggs in their original carton, so you are aware of the Best Before date, and to try and avoid storing your eggs in the fridge door, as this part of the fridge is most likely to incur fluctuations in temperature.
If there is anything else you'd like to know about storing your eggs, or general food safety questions, please leave a comment below and I'll do my best to answer all your questions.