Dealing with students one-on-one can be easier than in a group, since you can fine-tune your explanations to the individual. You have the opportunity to deal with students one-on-one during your consulting or office hours. One of your duties as a TA is to hold office or consulting hours.
The distinction between consulting and office hours is a matter of location. Office hours are held in 226A&B Sieg (the TA offices), while consulting usually implies time in a lab. Questions that are common in the lab are usually on a lower level, while deep confusion will usually be brought to a quiet room away from the terminals.
If you're dealing with someone caught in general confusion, its better to start with the basics and move up rather than try to see what part of a difficult concept he or she is missing. Chances are pretty good that he or she missed something a few weeks ago, that is now hindering progress. Sketches of control flow or data structures are usually helpful. Writing relevant terms, key words and drawing a graphical representation of what's going on can be a good idea, especially if English is a problem (whether the student's or yours!). Keep in mind that simply telling students the answer doesn't help as much as explaining how to get to an answer, then letting them try to work out a similar problem.
Avoid holding any kind of meeting with your students in your own office. Your office is shared, and the disturbance may not be appreciated by your officemates. The TA office, 226 Sieg, is shared by all of the TAs, to be used for office hours. The room is quite small, so we usually try to schedule our office hours so they do not conflict with the other TAs. You may schedule your office hours using MVis on the WWW ( http://www.cs.washington.edu/htbin-post/mvis/mvis/Room/Init). To get the hours you want, you must sign up early, so don't procrastinate!
You should discuss the number of hours you should hold with the instructor of the course, but a general guideline is to have two or three office hours per week. If they are never used by the students, you can generally always cut down by one. When you sign up for your time slots, bear in mind the times you think the students will be free and have time to come and see you. Times before 9am or after 4pm are generally times you will see few students coming to your office hours. Try to vary your hours from day to day so that different groups of students can attend. In the cases where some student(s) may not be able to see you during your regular hours, you should schedule separate appointments with them, provided it does not put undue strain on your time.
Since there is contention for the available time slots, you should stick to your times and not let your office hours run late. If you need more time you can either move to an empty class room, or if you know beforehand, reserve a room. This approach can also be followed for appointments.
If your office hours are consistently swamped, encourage students to go to professor's office hours. Frequently, students go to their TAs first. If so many people come to your office hours that you can't answer all of their questions, direct the students with more general questions about course material to the professor. Specific questions about homework problems or projects, grades, and the like are usually best handled by the TA.