The new site is location-aware, so you have an option to enter your location, so you get results related to where you are.
You can now create a mobile version for the personalized homepage right from your phone. Unfortunately, the list of options is limited to weather, stocks, movies and a list of popular news sites. But the good news is that the weather and movie listings are restricted to your location, which can be easily changed.
Because you've already told Google your location, you don't have to enter it each time you search. Here's a comparison between the old version of mobile search and the new one, for the query "pizza". Google shows 6 web results instead of 10 and the focus in on the business listings, which are targeted to my location.
You don't have to specify the type of search (local listings, for example), because the structure of the results is query-dependent. For some queries, you'll see image results or news articles at the top; for others, you'll see local results or only web results. Each section of search results can be expanded.
Another improvement can be found in web search results. Google optimizes the pages for mobile and splits them so you can easily read them on your mobile phone (that's not new), but now it sends you directly to the section that's most relevant to your query, highlights the query in the page, creates a table of contents for some of the pages and shows a link to the feed, so you can read it in Google Reader. That's pretty impressive.
If I search for "tea house google theme" and click on the result from Google Operating System, I'll read only the most relevant section of the page.
If you have a clever phone that knows how to handle web pages, you can deactivate Google's transcoder in the settings.
Google removed the option to search only mobile-optimized pages and merged them with the standard web pages. You'll notice that pages written for mobile phones have a small phone icon next to them in the search results.
All in all, there's an improvement. People can find more information relevant to them with fewer clicks (especially if they're in the US), but Google could have added unit conversations, mathematical calculations, facts, sport results, traffic information etc. For now, simple queries like "13*3.14" or "Italy population" don't return the right answer.
Google Mobile Search is available at google.com/m, although entering google.com into your mobile phone should work as well. You should see a link to try the new version at the top of the page.
Update: Here's a page where you can compare the old and the new version of Google Mobile Search with Yahoo Mobile Search and Windows Live.