How do most rookie teams find mentors/sponsorship? I know in some cases sponsors provide mentors but that doesn’t always seem to be the case. And advice for how to acquire sponsors/mentors/grants/funding/etc. in general? I’m new to this whole FRC thing and trying to get some advice 
Well, most of our mentors are also parents. We did it the other way around - got a sponsor through a mentor.
I highly recommend reaching out to a team in your area, they will be able to help with these things. We were helped tremendously by 525.
This. We’ve gotten more sponsorship through mentors than mentors through sponsors. You can find mentors at work, at the school, and even at church, but personal appeals are required. Don’t forget to find mentors for finding sponsors/fundraising, writing the chairman’s award paper, and making travel arrangements and such. When making these appeals, focus on the skills a prospective mentor DOES have; don’t let them wriggle out because they don’t know anything about robotics.
And even if they can’t identify mentors for you, they can help the mentors you do have get up to speed.
The best way to find sponsors is to go to the local companies in your area and ask if they would potentially be interested in sponsorship. Offer to present for them, they are a lot more likely to give you a shot by presenting for them instead of flooding their email. Typically when we present, we start out discussing our history and stats, then what we are currently doing, and then a coach steps in to explain why we need sponsors. Also when you do find sponsors maintain close relationships with them. Based on the level of sponsorship (amount of $) our sponsors provide we give them things in return like advertising on our robot, trailer, brochures, social media, etc. Eventually if you are close enough with your corporate sponsors they will help you find sponsors. Navistar recommend us to TE Connectivity for a sponsorship a while back. Also ask your teams family mentors who work for corporations to see if they can help find your team sponsorship.
We do a lot of outreach events and this has helped us get sponsors.
As an FLL team, your budgets are much smaller than FRC, so talking to local business and having them donate $100 or so is very feasible.
Be sure to have a pitch ready to give them as to why they should sponsor your team and be sure to follow up with them, let them know how your team is doing and invite them to your competition.
Like everyone else is saying, sponsors through mentors. Many mentors are parents, and they usually get their business involved, such as our programmers dad owns a machine servicing company, meaning he has tools and parts we can use. One of our builders’ dad’s work at a Tool and Die shop, meaning we can use their business for matching sometimes. I don’t think the team has ever got mentors from a sponsor.