You can use Kayak for looking up flights, however you will usually find the flights to be a little more expensive. The best website to use when booking flights is Skyscanner. They usually have the best discounts on flights and provides an easy to use site that can help in planning your trip, even if you don’t know your final destination yet! FYI they have both a .net and .com version Skyscanner/Skyscanner.
The best/cheapest airlines to use are Ryanair or easyjet (for Europe). You will find these airlines on Skyscanner or on Kayak, however you can try going directly to their websites for more accurate prices. Kayak will give you the best flights from more established airlines, while Skyscanner gives you a better view of all the possible types of flights, and often has deals with third parties that are unavailable on Kayak.
When using Ryanair or easy jet you must know that they have a VERY STRICT LUGGAGE POLICY. For easyjet you get to bring on one small luggage bag and if it doesn’t fit the dimensions you may pay any where from 30-70 Euros (40-100 USD). Ryanair lets you bring on 2 small carry on things I think and the same goes for the dimensions of this airline.
Another thing you must pay attention is YOU MUST PRINT OUT YOUR BOARDING PASS IN ADVANCE. If you forget to print it out, and ask them to print it out at the airport they may charge you 80 euros!!!! (For Ryanair or Easyjet)
The other option, the more 21stCentury option is to add your boarding pass to your phone. If you have an iphone, the new wallet function is fantastic. It allows you to add boarding passes, concert tickets, company rewards points cards, consolidating everything into one user friendly application. If you lose your wallet, you can use Apple Pay to buy things in stores, and unlike in the US, Europe brings out the card machines to your table, so theoretically you could pay with Apple Pay tableside which is something that would never happen in America. You can also use Apple Pay Cash to pay back friends who covered for you no matter what bank they have.
The flights on these airlines are cheap, but they can become very expensive if you don’t print out your boarding pass in advance and carry the right size luggage. Also, book your flights in advance and you will save a lot of money.