How does that work when the amount of the tax depends on the location? Do your visitors need to enter their billing & shipping information before they can browse your site?
VAT is uniform across all of Germany. Therefore detailed location information isn't necessary. The country can be inferred reasonably accurately from the IP. You can have a drop-down somewhere to correct the country if necessary.
~~And I don't think there's a law that requires you to show the price including tax, but it's definitely expected.~~ I have been corrected: it is indeed required.
> The country can be inferred reasonably accurately from the IP.
That would be a guess at best. A VPN or caching service (or merely inaccurate geo-IP data) could cause the site to infer the wrong location. The law linked by Vespasian doesn't appear to make any allowance for cases where the tax jurisdiction may be uncertain, though it's possible that the automated translation I read glossed over some nuance.
> You can have a drop-down somewhere to correct the country if necessary.
If the visitor neglects to select their country, and the default was incorrect, does that mean the site is not compliant with the law? The requirement was simply to show the final prices—no allowance was made, so far as I could tell, for being given inaccurate information.
As Vespasian said this law was written before consumers had large scale access to the internet and used it to order things online and from foreign countries.
In practice, if you're not a German business you probably don't need to worry about it too much. Most (if not all) countries in the EU have at least the custom of showing final prices including tax. If you're an EU business, you could just do that by default unless the customer explicitly specifies they are from elsewhere.
If you're a non-EU business selling to EU customers, you don't need to handle VAT. The customer is responsible for paying VAT upon import and will generally be notified by customs of the amount due before the item is released. Of course you can choose to handle VAT and make the customer's life easier, but you don't need to.
When I order something from Amazon.co.uk to Germany (post brexit) I see the normal price including British VAT on the product page. As soon as I add the item to the cart and go to checkout, VAT goes to 0% (doesn't apply because the item isn't sold in Britain) and I get an "Import Fee Deposit" added. The latter consists of German VAT and any applicable duties. This is because they handle dealing with customs on my behalf.
This law is an old one and has been in effect forever (offline and online). I'm certain there is a lot of legal practice and precedence on what can be expected of a "reasonable" company. Courts are usually quite pragmatic in their rulings (otherwise no law would ever work)
The Goal is to prevent misleading advertising and tricking of the customer by showing them a different price.
A typical costumer won't use a VPN etc, so if you can demonstrate that you had a sufficient amount of evidence no court will punish you for it.
E.g.: German IP, German browser, a German credit card and a German shipping address are probably sufficient.
Edit: it used to be that you have to go to great lengths to ensure that no consumer can shop in your B2B shop (like verifying their business license, making sure the customer isn't lying etc). In recent years the federal high court ruled on several occasions that this is not necessary and a simple disclaimer and a checkbox is enough in most cases (IANAL).
There are strange cases (e.g. I'm on holiday in Germany using hotel wifi, ordering from a German webshop for delivery to Sweden using a Danish credit card).
In that case, the price will change when the delivery/payment details are entered.
In many jurisdictions your advertised price (e.g. for German users on your german page) needs to include taxes.