This is an information sheet that I created for Find the Horcruxes when the topic of traveling in the wizarding world (particularly with the introduction of ID badges) came up.
There are several methods of travel in the wizarding world:
These are just the ones that are unique to the wizarding world that don't also exist (as a means of travel) in the muggle world. Of course, wizards can also take trains (such as the Hogwarts Express), cars, boats, and planes to visit other places.
Travel within the confines of Great Britain and Ireland (England, Wales, Scotland, Northern Ireland, Ireland; "The Isles") is comparatively unmonitored.
Apparation
You can apparate anywhere within the Isles (sans places that have anti-apparation wards or are unplottable, such as Hogwarts, certain islands, and Azkaban) within your own abilities (obviously, if you can't apparate more than 5 feet, you can't really get from south England to northern North Ireland in just one jump).
Broomstick
The most widely used and accepted form of magical transportation in the Isles. Though, of course, you can't exactly go flying over populated muggle areas on clear days/nights without being cited: if you're going to be flying over or through such areas, you must do so only under cover of cloud and/or fog, so that muggles can't look up and see someone flying past on a broom.
Floo
Any fireplace that is connected to the floo network has the potential to be flooed to. However, to prevent people from simply flooing into other people's homes to kill them or rob them, but still allow them to have their houses hooked up to the network, floo fireplaces in inhabited areas are "locked" and you cannot get in without permission. Likewise, the floo fireplaces into the Ministry of Magic building are locked after business hours, so you can only get in if you are in possession of a Ministry employee badge.
The Knight Bus
The Knight Bus is summoned by holding out your wand in your right hand. Yes, right hand. Left hand is for emergency use only. Oh, and watch out to make sure you don't get run over when the giant triple-decker purple bus appears nearly instantly. The bus travels in alphabetical order to requested destinations, and can travel between faraway places in a pop that is quite similar to apparation. The Knight Bus travels anywhere you want to go, as long as it's on land. It also does not travel outside of the Isles. During the day, the passengers have armchairs for seats; at night, the armchairs are replaced by brass beds.
Portkey
As long as you go through the paperwork required for a portkey, you can travel to just about anywhere within the Isles that's permitted (obviously you can't portkey straight to Hogwarts without permission from the school, or into someone's private residence, or smack dab into the centre of a busy muggle city square). The use of the Portus spell is regulated, so that citizens aren't going around turning everything into portkeys.
Travel outside of the Isles is slightly different than travel within.
Magicustoms
Every country (the Isles are collectively considered their own singular country) has an international border set up and a magicustoms station. If you try to go from one country to another by magical means, you will automatically be "bounced" to the magicustoms station for the country that you are trying to leave. You must pass through customs, where you will be subject to your luggage being searched (to ensure that you aren't trying to smuggle anything illegal into or out of the country). Probity probes are used to ensure that no spells of concealment or disguise are being used (both on the luggage and on the witches and wizards themselves). There are charms set up to detect bribes, and hitwizards are on location to ensure that nobody is trying to sneak (or bribe their way) through customs.
For the Isles' magicustoms station, it is run jointly by the Department of International Magical Cooperation and the Department of Magical Transportation.
Records are attempted to be kept at the magicustoms stations, but with (until recently) the lack of official identification, records could be incorrect (as there was, of course, no way to ensure that Howard Thomas actually is Howard Thomas and not Jerry Smith). Obviously, the more well-known or famous you are, the less likely it was that you would have been able to sneak through magicustoms with a psuedonym.
Once you have gone through magicustoms for the country you are leaving, you are able to travel to the magicustoms station for the country you are travelling to. There, you will once again have to go through their magicustoms station, and then you can go wherever you want in that country (within reason, of course).
Beginning Friday, January 15, 1980, any wizarding citizen of the Isles must show their valid ID at Magicustoms in order to leave the country or to reenter it. (At first) This is just to ensure that more accurate records are being kept. The requirement to show your valid ID at customs is the only change that has been made under the new travel rules that were announced January 1, 1980.