The Manifold way for that today is Release 8's IMS. It's very reliable and well-understood but it is not a good solution for bigger data beyond a few hundred MB.
Later this year, perhaps as soon as summer, Release 9's development path will reach the big "servers" releases that are planned, which include web serving. That will be perfect for what you want to do, because 9 can handle bigger data with good performance, 9 has way better styling capabilities, and 9 has a much broader understanding of web server interfaces than 8.
Web serving with 9 is also expected to be much simpler than with 8.
8 is one step evolved from the classic approach where there is a GIS package that creates projects for web display, and there is a different web server package. In the ESRI world, the classic analog is ArcGIS as the GIS and ArcIMS or whatever as the web server. In the open source world, the analog is QGIS and Map Server. In both cases, the GIS/IMS packages require an Internet server such as Microsoft IIS or Apache to host the web serving environment.
8 takes one step beyond that classic approach by integrating the GIS/IMS part with the GIS itself, so to run a web site you need just 8 running within IIS or Apache. That's great in that it eliminates integration issues between the GIS and the GIS/IMS since both are the same thing. But it still leaves the need to operate everything within IIS or Apache.
9 will take two steps beyond the classic GIS approach: 9 will fully integrate IMS and GIS and also include within 9 an integrated Internet server, so there will be no need to install/run/administer IIS or Apache. Any machine with a copy of 9 on it will automatically (if you allow it) be a web server for the 9 projects you want to make available on the web, on your local networks, etc.
Most likely, this will be a function of Viewer as well, so you could publish 9 .map projects for web browsing just by putting a free copy of Viewer on whatever machines host your web sites. That will eliminate any licensing issues that with 8 complicate GIS web serving from web sites on virtual servers, third party hosting companies, etc.