There are many FRC grants that teams can apply for. Some are for rookie teams in their first year, and others are open to rookies and veteran teams. Many grants have certain requirements for teams to meet before applying.
Team 353 The POBots and team 358 The Robotics Eagles have put together a collection of FRC grants here: FRC Grant Database
FIRST has many resources for funding ideas and examples that are linked here:
Stem + C Competition Grant
Henrico Education Foundation
How to find local sponsors:
Create a flyer with all the team's info (name, member count, affiliated school, FIRST level, etc.)
Then
Email local businesses explaining why you're emailing and ask if they are interested in sponsoring the team. DON'T forget to attach the flyer before sending the email.
Talk to a company in person. Take flyers with you.
Make a post on social media.
Talk to the parents of the students and ask if their companies would be willing to support the team.
Submit grant proposals