The usual caveat, folks: make sure your graphics and sound card drivers are up to date, and that you've installed the latest compatibility updates for Windows. These fixes have been tested on Windows 7 64-bit only, but may also work for other systems.
Like many great old games, Sacrifice is broken on modern systems.
The first thing you'll want to do is download the manual patch (direct link) and extract the files into your install directory, overwriting the existing files.
While you can increase your resolution to modern sizes, it's not suggested, as objects have a tendency of disappearing, making the game unplayable.
Nvidia owners only
The next step only applies to Nvidia graphics card owners. The first time you meet the peasants, you'll get graphical corruption and CPU hitting 100 per cent. To fix this, we need to create a custom profile with Nvidia Inspector, which will give us access to settings that are not usually in the Nvidia control panel.
Open the program and click the screwdriver and wrench icon to the right of the Driver Version entry. Now we can create a new profile for Sacrifice by clicking on the yellow star icon. Name it, then click OK. Two icons to the right of the yellow star is a square with a blue top and a green plus sign: click this, then browse to where Sacrifice is installed, select sacrifice.exe and hit OK — this associates the executable to the profile. If, somehow, the multiplayer servers are still running at sacrifice.kicks-ass.net, you'll want to add SacPro.exe to this as well.
Click the icon with the magnifying glass over the gears to show all available settings, then scroll down to the Unknown section and change the entry starting with PRE_D3D9_COMPATIBILITY_BITS to 0x00000040 (it's the first entry in the drop-down menu). Hit the Apply Changes button at the top right.