Encourage the student to constantly think out loud as he is solving a problem. This strategy serves two purposes. First, it allows the student to remember his steps because not only is he doing them, he is verbalizing each part of the solution. This will help his memory when solving problems independently. Second, it allows you to get into the student's mind. If a student is verbalizing steps and then falters or stumbles, you will know he has hit a roadblock and needs coaching. If he is just solving the problem silently, you will have no idea when he is confused or struggling. Having him constantly verbalize will give you a chance to help him when an issue arises, not when he is completely overwhelmed with the problem. Also, ask the student to verbalize any new concept you are teaching. Once he can tell you the idea in his own words, he is beginning to understand it.
Just because the session is one-on-one doesn't mean you need to stay seated. Use methods that encourage your student to move and to develop skills in fun ways. For example, if she is learning to add and subtract integers, have her walk up and down a number line. If she is learning multiplication facts, place numbers all around the room and have her jump to solutions as you call out math facts. Also, encourage your student to have fun with numbers. Draw pictures to help remember divisibility rules or cartoons that will help with definitions.
Children learn math well when they can physically see an abstract concept. Manipulatives help to serve this purpose. Melissa Stewart, a writer for scholastic.com, suggests uses for manipulatives at all levels. She suggests that a teacher use base 10 blocks, counting rods or even the student himself as a concrete tool. Stewart gives an example of a teacher who uses pennies to illustrate the concept of percents. The teacher has the student actually slide the penny one place to the left to illustrate 10 percent. When she "physically moves" the decimal point, the student will see the concept clearly. Another teacher uses fruit to teach fractions. Manipulatives can be useful for any level, with any student, and will help develop concrete understanding for abstract concepts.