Obtain valid passports for each member of the band and for each person traveling with the band.
Put together a digital press packet that includes photos, noteworthy performance dates, bios and any charity events you have played.
Determine how long you are going to stay and to which countries you are going to travel. Remember that while countries are close together in Europe -- they are not that close. You want a logical progression. It is not logical to be in London on Saturday, Italy on Monday and then back to France on Tuesday.
Map your route. Get an updated map of the region in which you want to travel and start planning your route.
Contact the state departments or embassies of the countries in which you want to perform and obtain artist visas for each country in which you want to perform. This is not always a quick process, so start early.
Research clubs in the cities in which you want to perform. Learn the hot neighborhoods and call some small to medium-size clubs. Ask to speak to the booking manager or the person who handles the artist bookings. Many people in Europe speak English, so if you do not speak the native languages of the countries you are calling, do not fake it. No matter the outcome of the call, ask for an e-mail address where you can forward your press release and bios.
Book charity events. Research charity events in the cities you are going to play and contact the person in charge of entertainment. Volunteer to play at one or two charities. This will give you instant European gigs to add to your resume and buy you credibility. When you call the clubs you can open with "We are going to be in town playing so-and-so charity event and we are looking to set up a couple of more dates." You will have an instant buy-in.
Call many places and don't give up. If you are building a name for yourself, it may take a while to fill your schedule...but being tenacious really does work.