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I'm going to be taking a trip to Germany in a few days. I will be in Munich and I was considering taking the train to somewhere in Austria (Innsbruck maybe?) so I could see the Alps.

I'm wondering how difficult it is to travel between countries for something like this? Do I need to go through the whole customs process or is it pretty much like traveling within Germany since they are both part of the EU?

Thanks for any information.

As long as you stay within the Schengen Area, you should be able to travel freely without any systematic passport checks, so in most cases, it looks exactly like domestic travel.

The Schengen Area is composed of 22 of the 28 EU member states, as well as some other non-EU states such as Switzerland. Germany and Austria are both part of the Schengen Area.

Random spot checks may still happen, and in some cases systematic checks have been temporarily re-introduced, mostly due to the migrant crisis, but also sometimes for security reasons. Switzerland is also known to have a peculiar interpretation of "no systematic checks".

Even if there are no checks at the border, you should still have your passport and other paperwork with you, as you may be checked in other circumstances.

You should always have your passport with you when out of your own country.  Within Schengen, you’ll not likely be asked for it, but it’s possible, and if you don’t have it when asked, definitely a hassle or worse.

You can probably book train trips on whatever site you use within Germany, but you can also easily do it at Loco.

There are probably other sites.  Rick Steves has some good informational pages about trains (and other travel info) in Europe.

Travelling regularly between Germany and Italy I usually get stopped at custom when entering Switzerland, a Schengen Area country but not part of the EU, but never happened when crossing Austria. There should not be any barrier except due diligence police controls on trains and at boarding in the train station.

Edit: corrected as Switzerland is actually part of Schengen Area but not part of EU
Schengen info

It is extremely easy and there is no check.

As a non-Schengen national I took the train between Austria and Germany twice in the last few months, and there was no suggestion that passports might be checked. I also took a bus tour that crossed the border and we were not even advised to bring passports. There are not normally checks when crossing the border between Schengen countries - that's the point of the Schengen area.