This is a common problem among many tutors, paid or volunteer. It's awfully tempting to just write out an answer for the student when they are really struggling to understand something, but this is usually a bad idea. What else can you do?
Go ahead and give them the answer! Don't make it a habit, but sometimes walking a student through a question is the easiest way to make him or her understand. This is especially true if you're not very comfortable with the material, or are just starting out as a tutor. Once you're more experienced, you learn how to present ideas to the students without giving everything away. Until then, don't worry about giving the first answer away, but don't let them just say "okay, that makes sense". Encourage them to try a similar question on their own, from scratch, until they can do it without your help.
Put the assigned questions away. Before you start going into your explanations, put assigned all the questions that the student is supposed to answer and come up with your own. This way, no matter how much of the question you give away to the student, they still have to go through the assigned questions on their own some other time.
Catch yourself. Keep reminding yourself before showing up for a tutorial session that the student needs to do the work. Pretend the professor is standing there making sure you don't give everything away. Some students are looking for someone to do their homework for them. As soon as you find yourself writing down or dictating lines which could end up in a final solution, you've gone too far.
Make the student do the talking. Instead of sitting there dictating entire lectures to the students, sit back and ask them what they know about the topic. Correct and expand on their ideas, but let them speak their minds. The same goes for writing. Leave the pen in the students' hands. If you find yourself trying to write things down for them, sit back and try to understand why the student is not writing what you would have written.
Meet in small groups. Sometimes it helps to tutor two or three students at the same time because they can work things out together. Suggest some ideas to the group and see what they can make of it. Often, the answers will come out without any explicit help from you. Many students who feel they need help just need some way to sort out their ideas on the topics that have been presented in the course. Give them a chance to do this.
The best advice here is to mix it up. Don't stick to the same formula every time you meet with a student or you'll get into a rut. All students learn in different ways, so try various combinations of these techniques to make things go smoothly. If one idea fails miserable, discuss it with the students and find out what more can be done. Many students are very much aware of their learning skills and can offer some suggestions. Students can be the best teachers!