Type in "best airfare alerts" to your preferred search engine. You may vary the words a bit to see how the search results change. For example, you can try "monitor best airfares."
Navigate to the websites that look most interesting to you. Be attentive to those with progressive information on the trends in getting airline alerts customized to your liking.
Follow instructions on each website you wish to register for price alerts, choosing to monitor all airlines or perhaps specifying particular airlines if that option is available. Note that alerts can be pushed to you with the latest web technologies such as RSS feeds and widgets. Research the use of these tools as needed for both your computer(s) and mobile phone.
Verify that fare alerts from the sites selected compare favorably one to another. If you begin to notice one site having consistently lower airfares, adjust your subscriptions to fare alerts accordingly.
Be ready with your credit or debit card to act quickly on a desired fare alert to lock it down. Airfare rates are subject to change literally within minutes! For any locked in airfare you purchase, continue to monitor alerts for lower fares so you're more attuned to timing, especially during peak travel periods. Also, take the moment you need to read any terms and conditions of the fare you purchase, as it will likely cost you dearly if any changes to the purchased itinerary have to be made.