Note: These instructions are generally for WebDAV servers only. You should never whitelist the Zotero sync server certificates unless you understand the consequences.
Zotero Standalone does not currently provide a graphical way to whitelist self-signed certificates of WebDAV servers, as is possible in Firefox.
If you use a WebDAV server with a self-signed certificate, you can open the WebDAV URL in Firefox, accept the certificate, and then copy the cert_override.txt file from the Firefox profile directory to the Zotero Standalone profile directory, located at one of the following paths:
Mac OS X:
/Users/<username>/Library/Application Support/Zotero/Profiles/<randomstring>
Windows Vista and 7:
C:\Users\<User Name>\AppData\Roaming\Zotero\Profiles\<randomstring>
Windows 2000 and XP:
C:\Documents and Settings\<username>\Application Data\Zotero\Profiles\<randomstring>
Most Linux distributions:
~/.zotero/Profiles/<randomstring>