You can download either the 32-bit or 64-bit version of UCINET. The 32-bit version is the standard version and runs on both 32-bit and 64-bit Windows. The 64-bit version is experimental and only runs on 64-bit windows. As it is subject to crashes, it is best used in tandem with the 32-bit version.
32-bit Installation Package. This installs the 32-bit version of UCINET along with several helper programs (such as NetDraw), and puts a copy of all the standard datasets in a folder called Ucinet Data under your My Documents folder. The installation program is new and unfortunately can't automatically uninstall versions of UCINET prior to 6.531, so you should do that yourself prior to installing 6.531.
64-bit installation package. If you have a 64-bit version of Windows, you can try this 64-bit version of UCINET. It lets you analyze much larger datasets, if you have the RAM memory for it. However, it is also flaky. Older parts of UCINET are not compatible with 64-bit execution, so these parts will crash. If when you try to run the program it complains about missing some files, download and extract these files to the UCINET folder: double64.zip. Also, here is an (older) version of the 64-bit exe -- no installation package: UCI6.exe. If you download this one, you definitely need to download the double64.zip file and extract the files to the same folder as uci6.exe
Trial vs "real" version. Actually, there is no separate trial version. If you download the program, it will run on your computer for 60 days without having to enter a registration code. Buying the program gets you that registration code. So whether you buy or just try, you download the same program.
Virus/malware issues. There was a time when the download files were stored in a DropBox location. For some reason, this caused Norton AntiVirus to flag the program as dangerous. So we don't use DropBox for this anymore. But you might still run into issues with Norton or some other anti-virus program when installing UCINET. One thing to be aware of is that Windows 8 will issue a warning that the publisher is unknown and probably dangerous. This just means we haven't sought (read: paid for) Microsoft certification.
Installation works best if you right-click on the installation file (typically called something like setup32UCI6534.exe) and choose 'Run as Administrator'. Similarly, it is also helpful to use 'Run as Administrator' when running UCINET itself for the first time, as this allows you to register the program for all users of your machine. See the FAQ on this.
The best way to run UCINET on a Mac is to use a Windows emulator such as Parallels (or, of course, Bootcamp). However, it is (often) possible to run UCINET on a Mac using Wine. For more information, see this FAQ.