Paying for seminary is a concern for many pre-seminary and seminary students alike. Unless you happen to be independently wealthy or a family friend of Bill Gates, financial concerns have to be addressed.
Perhaps the best strategy for getting funds for seminary is to excel at your undergraduate preparation. Most seminaries and divinity schools have scholarship or fellowship funds that are based completely on one's academic merit. You should have a "short list" of schools that you want to attend and need to investigate the availability of these funds, deadlines for applications, requirements, and so forth. On a personal note, I received a fellowship from Princeton Seminary that paid for *everything* while I was a student, so it is possible. Really!
Another source of income for seminary students are denominational scholarships and grants. Many mainline denominations have "deep pockets," so to speak. They will often have scholarship or grant funds available for students who are preparing for ministry in their specific denominations.
Sometimes, these funds require service to the church while other times they are gifts without restrictions. If you are a member of a large denomination (United Methodist, PCUSA, PCA, Southern Baptist, etc) it's worth checking out the funds available to those in your denomination. Some of the scholarships can be substantive.
In addition to scholarships, fellowships, and denominational funds, most seminaries have grant programs based on a student's demonstrated financial need. While you'll need to demonstrate need based on your tax returns and other documents, many seminaries have endowments that rival (or far exceed) colleges and universities. From personal experience, I can say that it's in your best interest to complete your seminary financial aid applications early.
If you have exhausted the possibility of grants, scholarships, and fellowships, you can consider taking out student loans. There are many types of loans available, perhaps the most popular being Federal Direct Loans. Two types are available - Subsidized and Unsubsidized. With a subsidized loan, the government pays the interest while you are enrolled in school; with an unsubsidized loan, you are responsible for the interest (either by paying it directly or having it added to the sum of your loan). Both loans have favorable interest rates.
Finally, many students work part-time to help paying for seminary. There are usually many on-campus jobs available; however, many students find it more profitable to work off campus, even beginning church work during seminary. You may also be able to do internships (which will likely be required anyway) that provide supplemental income.
Personally, I worked as a youth leader and a hospital chaplain during my second and third years of seminary, both of which were paid positions. If you wish to find work doing guest preaching or working with youth, music, or other education ministries, there's a good chance you'll find the opportunity.