The steps are pretty much the same as buying WITH a real estate agent only you don't have the assistance and advice of a professional. You find a home, make an offer, have the contract reviewed by attorneys for both the buyer and the seller, conduct home inspections, negotiate any issues raised in the inspection, do a title search, get a survey, obtain homeowners insurance, obtain a mortgage commitment, and close loan. It is much more complicated than it sounds and mistakes can be very costly.
You CAN use a real estate agent to buy a FSBO, however and I would strongly recommend doing that. You would simply enter into an 'exclusive buyer's representation agreement' with the agent of your choice. Generally such an agreement would provide that you will pay the agent if, and only if, the seller does not do so. Most FSBO sellers will pay an agent to bring them a buyer, but even if they don't, you would simply reduce your offer to account for the commission you have agreed to pay the agent. Believe me, it will be the best money you ever spent! Or, if the seller pays, DIDN'T spend! And, most real estate agents come with an entire TEAM that includes home inspectors, attorneys, mortgage professionals, and title insurance agencies, that will all work together to get you to the closing table with as little stress as possible.
Buying a home is probably the most expensive purchase you will ever make, and the process will probably be one of the most complex you ever experience, having a team of professionals on your side is crucial!