If you only need the functionality of one component, you can just install that component; however, all of the components rely on common code in the Horde package itself. Whether you install one component or all of them, you need to install Horde. So, if you just want to offer web-based email (the most common use of Horde applications thus far) you'd need to install Horde and IMP.
In response to the number of people that have asked this question the Horde Project has released pre-packaged versions of Horde with all the basics. Known as Horde Groupware and Horde Groupware - Webmail Edition these packages can greatly speed the deployment process. See http://www.horde.org for more information.
The Horde applications are free, having been released under the different open source licenses. Those of you familiar with open-source software can stop reading now. For those of you who are used to paying for software, no, we're not kidding, it's really free. And not only is it no-cost, but it's yours to modify and redistribute, too; the only restriction is that you can't turn around and make it not free. So, you can download Horde and components and install them on as many computers as you want, and let as many users as you want use it, without having to pay a penny to anyone, and you can make changes to the way it looks or operates, either for local use or for redistribution.
The Horde framework itself is even free-er, being released under the GNU Library General Public License. This basically means that you can use the Horde framework in proprietary programs; if you are considering doing this, please read the license, and, ideally, let us know.
Horde is developed on Unix, with the Apache web server, so it should certainly work on any Unix that you can build Apache and PHP on. Being written in PHP means that it should work anywhere that PHP works, though, so if you're not on Unix, please give it a try and let us know how things turn out!
Horde and all the Horde Components are known to work under Windows with Apache and PHP with acceptable performance. IMP and Turba, at least, are also believed to work on Windows with IIS and PHP.
The best place to turn after reading the documentation is to the appropriate mailing list for the component you're trying to install. Make sure you describe the problem clearly, including all error messages you might have received. Include the version of all the software you're using, including PHP, your web server, your database, any mail or LDAP servers you might be using, and, if the errors are occurring in use, what browser and OS are being used to access it.
Please do not contact the developers directly. They usually don't have time to deal with individual installations of Horde and its components, being too busy developing and FAQ-maintaining. (Besides, they're probably on the mailing list anyhow.)
Finally, there is also commercial support available, with the opportunity to hire Horde developers to install and customize Horde and the Horde applications, or develop custom extensions and modules.
We don't make Horde installation a hard task intentionally, we always try to make it easier. One of the strength of Horde and its applications, is the independency from the underlying platform and used backends. The address book Turba, for example, currently supports at least 5 different kinds of address book storages, and you can choose from no less than 24 backends for Horde authentication. This makes it possible to integrate Horde in a lot of environments and existing infrastructures, but it also requires more complex configuration. It's a trade off between flexibility and complexity.
In other words, there are millions (if not billions) of different ways to configure Horde based on your local configuration. Writing documentation that would cover every possible configuration option would be quite a chore for a large software company (i.e. Microsoft, IBM), let alone a volunteer effort with only a small group of core developers. So while always mindful that our documentation could be better (of course it could), we can't do it all by ourselves. It may be that your setup uses a driver/configuration that is somewhat rare and, therefore, there is a lack of concise documentation on how to configure the exact way you envision. But on the other hand, the simple fact that a driver/configuration exists for your bizarre setup is a testament to the ability of Horde to adapt to your local environment. And sharing your experiences with everyone else (through the wiki, mailing lists, etc.) after taking the time to figure out these configuration secrets is a fantastic way to give back to the community for using this free software.
Horde users are encouraged to join the announce list and the list specific to their module; those interested in getting their hands a little dirty might also wish to join the horde and dev lists. Those interested in knowing everything that's going on with Horde development might wish to join the machine-generated commits and bugs list, which report changes in the Git repository and in the bugs database.
Before you do anything, take a moment to read this article on bug reporting, and keep its comments in mind when reporting Horde bugs.
Having read that, report the bug in the Horde bug database. Be aware that the Bugs database is not a support forum - please make sure you are reporting a bug (i.e. the software doesn't work as expected) rather than a support question (i.e. unclear on how to setup a config file).
Be sure to describe exactly how to reproduce the bug (if you know), and include all error messages that appeared. Also, specify the versions of Horde, the Horde component exhibiting the bug, and all supporting applications (web server, PHP, database, mail server, etc.). Of course, developers love when bugs come with patches attached; but if you can't write PHP, or can't track down the bug, make sure you let us know about it!