The first and most pertinent question you need to ask your prospective realtor is, how long have you been in the business? Although years in the business does not necessarily determine the level of success they have had but it does let you know how much experience they have and therefore how savvy they can be on your behalf. This question should not discourage you from taking on a partnership with a new realtor either. Many of the new real estate agents on the market are initially mentored by a seasoned agent and this can be a winning combination for a buyer or seller.
Your second most important question will help you determine whether your realtor has the ability to negotiate your deal. When you ask them how their list price is versus their sales price you will instantly discover their working success ratios. If you are buying a house their ability to bring down the list price in order to enable you to purchase is a definite bonus. On the other hand if you are selling the agent needs to have the ability to find buyers willing to pay close to what you're asking. If they cannot do this than it is time to keep interviewing.
From here you can question them about their strategy for you and how they would handle multiple offers for either the house you're buying or the house you're selling. Each agent will have their own take on a strategy to help you achieve the real estate goals in your future and it is really a personal preference how you respond to their ideas and plans.
Lastly, once you have asked all your questions and made your decision to go ahead with your realtor do not forget to ask about the contract between the two of you. Before you sign anything take home a copy and inspect each clause to make sure you know what you're signing. Once the contract is signed you are attached to this realtor for whatever length of time the contract states to sign carefully.
Take these questions, add to them what you like and write them down if necessary in order to make sure nothing is missed during your one-on-one interview. From here you are ready to get started finding or selling your home of choice.