This is going to be highly dependent on the specific installer you're trying to run. Most vendors couldn't care less about making unattended deployment easy for admins. Your best bet is to try and find someone who's already done the work for you. The Package KB at AppDeploy.com is a great place to start in addition to their forums. You can also try searching the wiki at WPKG.org.
If all that fails, you will unfortunately have to dig in and figure out the problems yourself. Enable logging everywhere you can and be prepared to spend a lot of time scouring for specific errors. Tools like Orca for MSI editing and ProcMon can be invaluable.
SCCM packages run as SYSTEM by default. You should try manually running your package as local admin on a test box to see if it even works at all first. If that is successful without any user interaction, try it again running as SYSTEM using something like PsExec. Some installers make dumb assumptions about who will be running the installer or what pieces of that user's profile will exist.
Repackaging tools that create a new installer based on pre and post snapshots exist, but they can be expensive. They can also introduce their own problems.