The LSA (Local Security Authority) is one of the less well-documented NT subsystems. The rather crude samples on these pages are, one hopes, enough to get you started.
Documentation for the LSA APIs is in the file \mssdk\samples\win32\winnt\security\lsapriv\lsasamp\lsaapi.hlp; some Platform SDKs have that file in \mssdk\samples\WinBase\Security\WinNT\lsasamp\. Current versions of the Platform SDK (and MSDN) document large parts of LSA in the usual places. A KB search for "LsaOpenPolicy" also returns a few useful articles.
Finally, pay special attention on the handling of LSA_UNICODE_STRINGs; those and the doubly indirected pointers through which some functions return arrays of information structures seem to be the biggest stumbling blocks.
The samples:
 | LsaAddAccountRights |
| LsaEnumerateAccountRights |
| LsaEnumerateAccountsWithUserRight |
| LsaEnumerateTrustedDomains |
| LsaQueryInformationPolicy, LsaSetInformationPolicy get and change audit settings |
| LsaQueryInformationPolicy, determine domain membership |