Lynne:If you are starting from zero experience, I would highly recommend that you obtain a manual on fundraising to use as an ongoing reference. Even something like Fundraising for Dummies will probably be helpful for you.
You will need much more, readily accessible guidance than provided on this board. While a manual is static, at least you don't have to wait for answers.
I also recommend checking out the web site of Tony Poderis, a frequent contributor to this board. Tony has been a fundraiser for a long-time and has several excellent articles on his website that will provide good advice to you.
That said, trying to answer your original questions, any healthy non-profit has diversified revenue streams. Such a nonprofit may be generating revenue through a fee-for-service structure, contracts with municipalities or gov't agencies, grants and, probably most importantly, private donations. A new nonprofit probably can't establish all of these revenue streams in its first years but you should consider whether they are possible in your future.
Also, these basic revenue streams can take many different shapes and costs so you will need to carefully consider your capacity to undertake them. For instance,
Service fees: the nonprofit might have a cleaning service, or perhaps a museum has a gift shop. This revenue goes back into programming.
Contracts: the nonprofit might enter formal agreements with gov't entities or even for-profits to perform specific activities/services, like vocational or GED training.
Grants: the nonprofit secures grants to initiate a new program.
Private Donations: This could encompass everything from direct-mailing, person-to-person solicitation; and bequests.
Sponsorships: a for-profit corporation provides funds to sponsor specific events or activities of the nonprofit.
How you decide your strategy - where you want to devote your energies - requires knowing far more about your nonprofit and its resources. Perhaps more consultation than a board like this can provide. Again, obtain a fundraising or how-to-run-a-nonprofit manual for your future reference. Determine if any local groups sponsor workshops on fundraising or nonprofit leadership; those types of things could also help you build good relationships with other agencies.
Above all, good luck.