In a nutshell, there are many categories of grants: federal, state, corporate, foundation and alternative sources. Each one presents pros and cons, such as ease of applying versus poor chance of winning. Start your search simply and locally, and then widen it in expanding circles until you hit the jackpot.
For example: Check with school district administrators about existing budgets or unspent fund balances towards the end of the fiscal year. It may be possible to re-purpose funds or combine balances. Then look to local corporations, foundations and philanthropists for monetary or in-kind donations. That’s the low-hanging fruit. In the meantime, pursue federal and state Department of Education grants for large-scale projects. Be aware, however, that government grants are extremely competitive, the application process is daunting, and the lead time is lengthy. In addition, DonorsChoose.org and other alternative sources of funding for educators are worth a try: major corporations do grant wishes here!