What is involved in regards to driving between EU countries? Do you go through passport control and immigrations? What about on a train? I have never traveled directly from one EU country to another. Thanks for the help!

Get out the appropriate map.

Start the car, put it in gear, and signal to get out of the parking space.

Get on the appropriate road.

If it is an autobahn, stay in the right lane except when passing and immediately get out of the passing lane when you see what looks like landing lights in the rear mirror. Its not a plane, just a high performance vehicle approaching at 250 kph.

Drive to your destination. Driving in the EU is just like driving from Boston to San Francisco except that in some countries one can get beer at the rest stops and gasoline costs more than twice as much as in the U.S.

Trains are just like going from Washington to Boston. Is there a customs check at the New Jersey border?

This depends on the countries involved. The Schengen agreement brought a (non-contiguous) free travel zone to many EU (and some non-EU) countries. In this case, there's very little in the way of checks. They can ask for ID, but this does not need to be a passport (unless local laws mandate passport as ID for non-nationals). Checks here are very cursory, if at all. I've walked over the France-Belgium border and France-Germany borders, and not even seen a soul. If you're off the main roads, you'll hardly be able to tell you've crossed a border. You can get the train from Amsterdam to Paris without even seeing someone in uniform.

To the non-Schengen countries, it varies. The UK is generally very strict, so if you take a ferry or the Tunnel, you'll see plenty of police around. The borders to (and between) the new EU countries tend to be far more heavily controlled. A visit to the border station at Bratislava-Petrzalka is an introduction to this...

Between non-Schengen countries in the EU (or in Western Europe) on the train, it depends on the arrangement. You may have immigration and/or customs at the departure point, the destination, on the train, or any combination of all these. For example, the Eurostar (London-Paris/Brussels) can have all three. Basel (in Switzerland) has railway stations with platforms that are French and German territory. Or you could meet the mobile officers (like going into Slovenia), complete with their laptops, scanners and mobile phone links to central computers.

Many car hire companies are less than happy for you to take your hire car to the new EU states. And that means you're not insured there, and the border guards certainly look out for that.

An interesting feature of some of the borders (e.g. Austria-Czech) are some no-mans-lands which the more enterprising 'grey market' traders (and calling it grey market is *very* generous) use to their advantage to sell tax-free (and often really rather illegal) goods.

Between EU countries, there is no customs control. However, they do have the right to stop and search you for any illegal substances you may be carrying.

Schengen is not the only free travel zone - there are some reciprocal arrangements, such as the UK and Ireland.

And don't forget the non-EU countries that are in the middle of it all. Switzerland, for example. Or (bizarrely), the Channel Islands are not EU, despite being part of the UK.

Spent vacation driving around the EU's Benelux countries, France, Monaco and Italy last summer/fall. No customs checks or even immigration checks although at the Swiss-Italian or Swiss-French border the passport may have been looked at in a very cursory manner (I don't recollect exactly, so maybe it wasn't examined at all).

To elaborate on earlier postings, Schengen countries are Norway, Sweden, Denmark, Finland, Germany, Austria, Netherlands, Belgium, Luxembourg, France, Spain, Portugal, Italy and Greece. Between these countries there are generally no border checks, though you occasionally hear travel advisories about Country X or Country Y reintroducing border checks for a limited period (e.g., I believe that Portugal was carrying out border checks during Euro 2004).

For those requiring visas there is now a single "Schengen Countries" visa, so a visa issued by one country will also get you into the others.

None of the new EU countries have joined Schengen yet, so crossing the border into Poland or Slovenia is like crossing from the USA to Canada or Mexico - i.e., you drive up to a checkpoint, you wind down your window and you present your passport (or national identity card if you are a citizen of an EU country that issues them).

As already mentioned the UK and Ireland aren't part of Schengen, so normal passport controls apply when arriving from another EU country. However, the British Isles have their own free travel area known as the "Common Travel Area" or (CTA). The five territories that make up the CTA are Great Britain (i.e., the big island that contains England, Scotland and Wales), the Republic of Ireland, Northern Ireland, the Isle of Man and the Channel Islands. I believe that in theory the CTA arrangements only apply to those who are citizens of the places concerned and that others need to carry passports when travelling - say - between England and the Channel Islands, but in practice there are never any checks.

Some non-Schengen countries have traditionally been quite lax at their road border crossings - it is fairly common to just be waved in and out of Switzerland without having to show any ID documents (though this only applies when crossing by car, there are always checks on the trains and when crossing into Switzerland on the Lake Constance ferries)

You HAVE TO be insured at least third party, since car insurance is EU-wide, so I doubt anyone has ever been stopped at the border because of that. And I am guessing that the fact that the rental contract may not allow you to take the car out of countries XYZ (old EU+Switzerland or something) won't interest border police that much either.
For the record, I've crossed the Italo-Swiss border without any control but was asked for travel documents after a Greece-Italy ferry crossing and frowned upon when I gave'em my Greek ID card instead of the passport they were expecting to see.

Less than happy is a bit of an understatement--it's a flat-out violation of the rental agreement. And it's not just New EU states--Hertz and Avis in Germany and Switzerland, for example, often won't allow cars (particularly expensive ones) to be taken to Italy or Spain.

The costs of one-way rentals vary widely according to the countries involved, and there are some interesting wrinkles: at Geneva, for example, it's possible to rent a car in either the French or the Swiss part of the airport, with massive impact on the cost of returning the car to, say, Paris.