How to properly leverage contacts when applying for jobs?

I'm slightly confused on how I should be properly using my contacts and relationships that I've established through networking to my advantage when I start applying for full-time roles. Do I update them after I've applied or after I had my first round? Should I ask for a resume push? When should I be asking them for interview advice or insights into the process? Basically what's the best way they can help me either land that first round or give me a leg-up in the interview process without me asking for too much?

I just don't want all the effort I've put into networking to amount to nothing, that would be pretty depressing considering I've poured hours into reaching out and calling people. Any advice or guidance would be appreciated.