First Time Flying Within Europe - Any Tips?

First off, absolutely understand their rules for luggage, check-in etc. One the ways they make up for the cheap airfare is to charge your for everything. Excessive luggage is very expensive. Also understand you may be using some remote airports and the transportation to where you want to go may be limited. Flying between European countries is no difference than flying between states.

If you're taking a cell phone, make sure all the airlines have the number and that you've enabled communication on their websites if necessary. I've been texted with gate changes and time changes and while annoying, it saved my trip once.
Also, keep checking the airline and gate displays to insure your flight hasn't been moved to another even after checkin.

Monique, As Frank mentioned, it's a good idea to pack light or you'll be paying expensive "overweight luggage" fees. Be sure to check their website for the current weight limits. In my experience, EasyJet is a bit more reasonable to deal with than some of the other budget airlines. The other important rule that you'll need to remember is that in Europe, you'll be allowed ONE carry-on article only. This doesn't mean one item plus a personal item such as a Purse, it means ONE ITEM ONLY of the approved size and weight. If there's any question about the size, the luggage will be placed in a sizing frame. If it doesn't fit, you could have a problem. I observed that very situation on an EasyJet flight from Rome to Athens last year. The carry-on bag of one of the passengers was too large to fit the frame, and a huge argument ensued. The flight crew eventually got involved, and told the passenger "I decide what goes on this aircraft, and that bag is not going". I never did find out how it was resolved? Finally, budget airlines don't always allow seat selection so if you're at the end of the line, you'll have to take whichever seats are available. Happy travels!